 10.10.1: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.2: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.3: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.4: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.5: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.6: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.7: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.8: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.9: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.10: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.11: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.12: Find the vertex, focus, and directrix of the parabola. Sketch its g...
 10.10.13: Find an equation for the parabola shown in the figure.
 10.10.14: Find an equation for the parabola shown in the figure.
 10.10.15: Find an equation for the parabola shown in the figure.
 10.10.16: Find an equation for the parabola shown in the figure.
 10.10.17: Find an equation for the parabola shown in the figure.
 10.10.18: Find an equation for the parabola shown in the figure.
 10.10.19: Find an equation for the parabola shown in the figure.
 10.10.20: Find an equation for the parabola shown in the figure.
 10.10.21: Find an equation of the parabola that satisfies the given condition...
 10.10.22: Find an equation of the parabola that satisfies the given condition...
 10.10.23: Find an equation of the parabola that satisfies the given condition...
 10.10.24: Find an equation of the parabola that satisfies the given condition...
 10.10.25: Find an equation of the parabola that satisfies the given condition...
 10.10.26: Find an equation of the parabola that satisfies the given condition...
 10.10.27: Find an equation of the parabola that satisfies the given condition...
 10.10.28: Find an equation of the parabola that satisfies the given condition...
 10.10.29: Find an equation of the parabola that satisfies the given condition...
 10.10.30: Find an equation of the parabola that satisfies the given condition...
 10.10.31: Find an equation of the parabola that satisfies the given condition...
 10.10.32: Find an equation of the parabola that satisfies the given condition...
 10.10.33: Find an equation of the parabola that satisfies the given condition...
 10.10.34: Find an equation of the parabola that satisfies the given condition...
 10.10.35: Find an equation of the parabola that satisfies the given condition...
 10.10.36: Find an equation of the parabola that satisfies the given condition...
 10.10.37: Find an equation for the set of points in an xyplane that are equi...
 10.10.38: Find an equation for the set of points in an xyplane that are equi...
 10.10.39: Find an equation for the set of points in an xyplane that are equi...
 10.10.40: Find an equation for the set of points in an xyplane that are equi...
 10.10.41: Find an equation for the indicated half of the parabola. Lower half of
 10.10.42: Find an equation for the indicated half of the parabola. Upper half of
 10.10.43: Find an equation for the indicated half of the parabola. Right half of
 10.10.44: Find an equation for the indicated half of the parabola. Left half of
 10.10.45: Find an equation for the indicated half of the parabola. Upper half of
 10.10.46: Find an equation for the indicated half of the parabola. Lower half of
 10.10.47: Find an equation for the indicated half of the parabola. Left half of
 10.10.48: Find an equation for the indicated half of the parabola. Right half of
 10.10.49: Determine whether the graph of the equation is the upper, lower, le...
 10.10.50: Determine whether the graph of the equation is the upper, lower, le...
 10.10.51: Determine whether the graph of the equation is the upper, lower, le...
 10.10.52: Determine whether the graph of the equation is the upper, lower, le...
 10.10.53: Find an equation for the parabola that has a vertical axis and pass...
 10.10.54: Find an equation for the parabola that has a vertical axis and pass...
 10.10.55: Find an equation for the parabola that has a horizontal axis and pa...
 10.10.56: Find an equation for the parabola that has a horizontal axis and pa...
 10.10.57: Telescope mirror A mirror for a reflecting telescope has the shape ...
 10.10.58: Antenna dish A satellite antenna dish has the shape of a paraboloid...
 10.10.59: Searchlight reflector A searchlight reflector has the shape of a pa...
 10.10.60: Flashlight mirror A flashlight mirror has the shape of a paraboloid...
 10.10.61: Receiving dish A sound receiving dish used at outdoor sporting even...
 10.10.62: Receiving dish Work Exercise 61 if the receiver is 9 inches from th...
 10.10.63: Parabolic reflector (a) The focal length of the (finite) paraboloid...
 10.10.64: Confocal parabolas The parabola has its focus at the origin and axi...
 10.10.65: Jodrell Bank radio telescope A radio telescope has the shape of a p...
 10.10.66: Satellite path A satellite will travel in a parabolic path near a p...
 10.10.67: Graph the equation.
 10.10.68: Graph the equation.
 10.10.69: Graph the parabolas on the same coordinate plane, and estimate the ...
 10.10.70: Graph the parabolas on the same coordinate plane, and estimate the ...
 10.10.2.1: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.2: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.3: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.4: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.5: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.6: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.7: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.8: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.9: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.10: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.11: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.12: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.13: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.14: Find the vertices and foci of the ellipse. Sketch its graph, showin...
 10.10.2.15: Find an equation for the ellipse shown in the figure.
 10.10.2.16: Find an equation for the ellipse shown in the figure.
 10.10.2.17: Find an equation for the ellipse shown in the figure.
 10.10.2.18: Find an equation for the ellipse shown in the figure.
 10.10.2.19: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.20: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.21: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.22: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.23: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.24: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.25: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.26: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.27: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.28: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.29: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.30: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.31: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.32: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.33: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.34: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.35: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.36: Find an equation for the ellipse that has its center at the origin ...
 10.10.2.37: Find the points of intersection of the graphs of the equations. Ske...
 10.10.2.38: Find the points of intersection of the graphs of the equations. Ske...
 10.10.2.39: Find the points of intersection of the graphs of the equations. Ske...
 10.10.2.40: Find the points of intersection of the graphs of the equations. Ske...
 10.10.2.41: Find an equation for the set of points in an xyplane such that the...
 10.10.2.42: Find an equation for the set of points in an xyplane such that the...
 10.10.2.43: Find an equation for the set of points in an xyplane such that the...
 10.10.2.44: Find an equation for the set of points in an xyplane such that the...
 10.10.2.45: Find an equation for the ellipse with foci F and that passes throug...
 10.10.2.46: Find an equation for the ellipse with foci F and that passes throug...
 10.10.2.47: Find an equation for the indicated half of the ellipse. Left half of
 10.10.2.48: Find an equation for the indicated half of the ellipse.Right half of
 10.10.2.49: Find an equation for the indicated half of the ellipse.Upper half of
 10.10.2.50: Find an equation for the indicated half of the ellipse.Lower half of
 10.10.2.51: Determine whether the graph of the equation is the upper, lower, le...
 10.10.2.52: Determine whether the graph of the equation is the upper, lower, le...
 10.10.2.53: Determine whether the graph of the equation is the upper, lower, le...
 10.10.2.54: Determine whether the graph of the equation is the upper, lower, le...
 10.10.2.55: Determine whether the graph of the equation is the upper, lower, le...
 10.10.2.56: Determine whether the graph of the equation is the upper, lower, le...
 10.10.2.57: Determine whether the graph of the equation is the upper, lower, le...
 10.10.2.58: Determine whether the graph of the equation is the upper, lower, le...
 10.10.2.59: Dimensions of an arch An arch of a bridge is semielliptical, with m...
 10.10.2.60: Designing a bridge A bridge is to be constructed across a river tha...
 10.10.2.61: Earths orbit Assume that the length of the major axis of Earths orb...
 10.10.2.62: Mercurys orbit The planet Mercury travels in an elliptical orbit th...
 10.10.2.63: Elliptical reflector The basic shape of an elliptical reflector is ...
 10.10.2.64: Lithotripter operation A lithotripter of height 15 centimeters and ...
 10.10.2.65: Whispering gallery The ceiling of a whispering gallery has the shap...
 10.10.2.66: Oval design An artist plans to create an elliptical design with maj...
 10.10.2.67: The planets move around the sun in elliptical orbits. Given the sem...
 10.10.2.68: The planets move around the sun in elliptical orbits. Given the sem...
 10.10.2.69: Graph the ellipses on the same coordinate plane, and estimate their...
 10.10.2.70: Graph the ellipses on the same coordinate plane, and estimate their...
 10.10.2.71: Graph the ellipses on the same coordinate plane, and estimate their...
 10.10.2.72: Graph the ellipses on the same coordinate plane, and estimate their...
 10.10.3.1: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.2: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.3: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.4: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.5: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.6: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.7: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.8: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.9: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.10: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.11: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.12: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.13: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.14: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.15: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.16: Find the vertices, the foci, and the equations of the asymptotes of...
 10.10.3.17: Find an equation for the hyperbola shown in the figure.
 10.10.3.18: Find an equation for the hyperbola shown in the figure.
 10.10.3.19: Find an equation for the hyperbola shown in the figure.
 10.10.3.20: Find an equation for the hyperbola shown in the figure.
 10.10.3.21: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.22: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.23: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.24: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.25: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.26: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.27: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.28: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.29: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.30: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.31: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.32: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.33: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.34: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.35: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.36: Find an equation for the hyperbola that has its center at the origi...
 10.10.3.37: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.38: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.39: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.40: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.41: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.42: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.43: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.44: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.45: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.46: Identify the graph of the equation as a parabola (with vertical or ...
 10.10.3.47: Find the points of intersection of the graphs of the equations. Ske...
 10.10.3.48: Find the points of intersection of the graphs of the equations. Ske...
 10.10.3.49: Find the points of intersection of the graphs of the equations. Ske...
 10.10.3.50: Find the points of intersection of the graphs of the equations. Ske...
 10.10.3.51: : Find an equation for the set of points in an xyplane such that t...
 10.10.3.52: : Find an equation for the set of points in an xyplane such that t...
 10.10.3.53: : Find an equation for the set of points in an xyplane such that t...
 10.10.3.54: : Find an equation for the set of points in an xyplane such that t...
 10.10.3.55: Find an equation for the hyperbola with foci F and that passes thro...
 10.10.3.56: Find an equation for the hyperbola with foci F and that passes thro...
 10.10.3.57: Find an equation for the indicated part of the hyperbola.Lower bran...
 10.10.3.58: Find an equation for the indicated part of the hyperbola.Upper bran...
 10.10.3.59: Find an equation for the indicated part of the hyperbola. Left bran...
 10.10.3.60: Find an equation for the indicated part of the hyperbola.Right bran...
 10.10.3.61: Find an equation for the indicated part of the hyperbola. Right hal...
 10.10.3.62: Find an equation for the indicated part of the hyperbola.Left halve...
 10.10.3.63: Find an equation for the indicated part of the hyperbola.Upper halv...
 10.10.3.64: Find an equation for the indicated part of the hyperbola.v
 10.10.3.65: Describe the part of a hyperbola given by the equation.
 10.10.3.66: Describe the part of a hyperbola given by the equation.
 10.10.3.67: Describe the part of a hyperbola given by the equation.
 10.10.3.68: Describe the part of a hyperbola given by the equation.
 10.10.3.69: Describe the part of a hyperbola given by the equation.
 10.10.3.70: Describe the part of a hyperbola given by the equation.
 10.10.3.71: Describe the part of a hyperbola given by the equation.
 10.10.3.72: Describe the part of a hyperbola given by the equation.
 10.10.3.73: The graphs of the equationsandare called conjugate hyperbolas. Sket...
 10.10.3.74: Find an equation of the hyperbola with foci and vertices , where and
 10.10.3.75: Cooling tower A cooling tower, such as the one shown in the figure,...
 10.10.3.76: Airplane maneuver An airplane is flying along the hyperbolic path i...
 10.10.3.77: Locating a ship A ship is traveling a course that is 100 miles from...
 10.10.3.78: Design of a telescope The Cassegrain telescope design (dating back ...
 10.10.3.79: Graph the hyperbolas on the same coordinate plane, and estimate the...
 10.10.3.80: Graph the hyperbolas on the same coordinate plane, and estimate the...
 10.10.3.81: Graph the hyperbolas on the same coordinate plane, and determine th...
 10.10.3.82: Graph the hyperbolas on the same coordinate plane, and determine th...
 10.10.3.83: Comets path Comets can travel in elliptical, parabolic, or hyperbol...
 10.10.4.1: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.2: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.3: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.4: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.5: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.6: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.7: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.8: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.9: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.10: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.11: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.12: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.13: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.14: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.15: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.16: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.17: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.18: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.19: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.20: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.21: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.22: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.23: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.24: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.25: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.26: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.27: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.28: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.29: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.30: Find an equation in x and y whose graph contains the points on the ...
 10.10.4.31: (a) Describe the graph of a curve C that has the parametrization(b)...
 10.10.4.32: (a) Describe the graph of a curve C that has the parametrization(b)...
 10.10.4.33: Curves , , , and are given parametrically, for t in . Sketch their ...
 10.10.4.34: Curves , , , and are given parametrically, for t in . Sketch their ...
 10.10.4.35: The parametric equations specify the position of a moving point P(x...
 10.10.4.36: The parametric equations specify the position of a moving point P(x...
 10.10.4.37: Show that,; are parametric equations of an ellipse with center and ...
 10.10.4.38: Show that,; and are parametric equations of a hyperbola with center...
 10.10.4.39: (a) Find three parametrizations that give the same graph as the giv...
 10.10.4.40: (a) Find three parametrizations that give the same graph as the giv...
 10.10.4.41: Refer to the equations in (1) of Example 6. Find the range and maxi...
 10.10.4.42: Refer to the equations in (1) of Example 6. Find the range and maxi...
 10.10.4.43: Refer to the equations in (1) of Example 6. Find the range and maxi...
 10.10.4.44: Refer to the equations in (1) of Example 6. Find the range and maxi...
 10.10.4.45: Refer to Example 7. (a) Describe the Lissajous figure given by and ...
 10.10.4.46: Shown in the figure is the Lissajous figure given by , ; . Find the...
 10.10.4.47: Lissajous figures are used in the study of electrical circuits to d...
 10.10.4.48: Lissajous figures are used in the study of electrical circuits to d...
 10.10.4.49: Lissajous figures are used in the study of electrical circuits to d...
 10.10.4.50: Lissajous figures are used in the study of electrical circuits to d...
 10.10.4.51: Graph the Lissajous figure in the viewing rectangle [1, 1] by [1, 1...
 10.10.4.52: Graph the Lissajous figure in the viewing rectangle [1, 1] by [1, 1...
 10.10.4.53: A circle C of radius b rolls on the outside of the circle , and . L...
 10.10.4.54: If the circle C of Exercise 53 rolls on the inside of the second ci...
 10.10.4.55: If in Exercise 53, find parametric equations for the epicycloid and...
 10.10.4.56: The radius of circle B is onethird that of circle A. How many revo...
 10.10.4.57: Graph the curve.
 10.10.4.58: Graph the curve.
 10.10.4.59: Graph the curve.
 10.10.4.60: Graph the curve.
 10.10.4.61: Graph the given curves on the same coordinate plane, and describe t...
 10.10.4.62: Graph the given curves on the same coordinate plane, and describe t...
 10.10.4.63: Graph the given curves on the same coordinate plane, and describe t...
 10.10.4.64: Graph the given curves on the same coordinate plane, and describe t...
 10.10.5.1: Which polar coordinates represent the same point as ?
 10.10.5.2: Which polar coordinates represent the same point as ?
 10.10.5.3: Change the polar coordinates to rectangular coordinates.
 10.10.5.4: Change the polar coordinates to rectangular coordinates.
 10.10.5.5: Change the polar coordinates to rectangular coordinates.
 10.10.5.6: Change the polar coordinates to rectangular coordinates.
 10.10.5.7: Change the polar coordinates to rectangular coordinates.
 10.10.5.8: Change the polar coordinates to rectangular coordinates.
 10.10.5.9: Change the rectangular coordinates to polar coordinates with and
 10.10.5.10: Change the rectangular coordinates to polar coordinates with and
 10.10.5.11: Change the rectangular coordinates to polar coordinates with and
 10.10.5.12: Change the rectangular coordinates to polar coordinates with and
 10.10.5.13: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.14: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.15: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.16: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.17: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.18: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.19: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.20: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.21: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.22: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.23: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.24: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.25: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.26: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.27: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.28: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.29: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.30: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.31: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.32: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.33: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.34: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.35: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.36: Find a polar equation that has the same graph as the equation in x ...
 10.10.5.37: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.38: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.39: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.40: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.41: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.42: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.43: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.44: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.45: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.46: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.47: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.48: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.49: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.50: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.51: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.52: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.53: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.54: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.55: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.56: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.57: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.58: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.59: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.60: Find an equation in x and y that has the same graph as the polar eq...
 10.10.5.61: Sketch the graph of the polar equation.
 10.10.5.62: Sketch the graph of the polar equation.
 10.10.5.63: Sketch the graph of the polar equation.
 10.10.5.64: Sketch the graph of the polar equation.
 10.10.5.65: Sketch the graph of the polar equation.
 10.10.5.66: Sketch the graph of the polar equation.
 10.10.5.67: Sketch the graph of the polar equation.
 10.10.5.68: Sketch the graph of the polar equation.
 10.10.5.69: Sketch the graph of the polar equation.
 10.10.5.70: Sketch the graph of the polar equation.
 10.10.5.71: Sketch the graph of the polar equation.
 10.10.5.72: Sketch the graph of the polar equation.
 10.10.5.73: Sketch the graph of the polar equation.
 10.10.5.74: Sketch the graph of the polar equation.
 10.10.5.75: Sketch the graph of the polar equation.
 10.10.5.76: Sketch the graph of the polar equation.
 10.10.5.77: Sketch the graph of the polar equation.
 10.10.5.78: Sketch the graph of the polar equation.
 10.10.5.79: Sketch the graph of the polar equation.
 10.10.5.80: Sketch the graph of the polar equation.
 10.10.5.81: Sketch the graph of the polar equation.
 10.10.5.82: Sketch the graph of the polar equation.
 10.10.5.83: Sketch the graph of the polar equation.
 10.10.5.84: Sketch the graph of the polar equation.
 10.10.5.85: Sketch the graph of the polar equation.
 10.10.5.86: Sketch the graph of the polar equation.
 10.10.5.87: Sketch the graph of the polar equation.
 10.10.5.88: Sketch the graph of the polar equation.
 10.10.5.89: Sketch the graph of the polar equation.
 10.10.5.90: Sketch the graph of the polar equation.
 10.10.5.91: Sketch the graph of the polar equation.
 10.10.5.92: Sketch the graph of the polar equation.
 10.10.5.93: Sketch the graph of the polar equation.
 10.10.5.94: Sketch the graph of the polar equation.
 10.10.5.95: If and are points in an plane, use the law of cosines to prove that
 10.10.5.96: Prove that the graph of each polar equation is a circle, and find i...
 10.10.5.97: Refer to Exercise 85 in Section 5.6. Suppose that a radio station h...
 10.10.5.98: Refer to Exercise 85 in Section 5.6. Suppose that a radio station h...
 10.10.5.99: Graph the polar equation for the indicated values of , and use the ...
 10.10.5.100: Graph the polar equation for the indicated values of , and use the ...
 10.10.5.101: Graph the polar equations on the same coordinate plane, and estimat...
 10.10.5.102: Graph the polar equations on the same coordinate plane, and estimat...
 10.10.6.1: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.2: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.3: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.4: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.5: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.6: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.7: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.8: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.9: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.10: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.11: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.12: Find the eccentricity, and classify the conic. Sketch the graph, an...
 10.10.6.13: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.14: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.15: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.16: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.17: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.18: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.19: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.20: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.21: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.22: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.23: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.24: Find equations in x and y for the polar equations in Exercises 112.
 10.10.6.25: Find a polar equation of the conic with focus at the pole that has ...
 10.10.6.26: Find a polar equation of the conic with focus at the pole that has ...
 10.10.6.27: Find a polar equation of the conic with focus at the pole that has ...
 10.10.6.28: Find a polar equation of the conic with focus at the pole that has ...
 10.10.6.29: Find a polar equation of the conic with focus at the pole that has ...
 10.10.6.30: Find a polar equation of the conic with focus at the pole that has ...
 10.10.6.31: Find a polar equation of the conic with focus at the pole that has ...
 10.10.6.32: Find a polar equation of the conic with focus at the pole that has ...
 10.10.6.33: Find a polar equation of the parabola with focus at the pole and th...
 10.10.6.34: Find a polar equation of the parabola with focus at the pole and th...
 10.10.6.35: An ellipse has a focus at the pole with the given center C and vert...
 10.10.6.36: An ellipse has a focus at the pole with the given center C and vert...
 10.10.6.37: Keplers first law Keplers first law asserts that planets travel in ...
 10.10.6.38: Keplers first law Refer to Exercise 37. The dwarf planet Pluto trav...
 10.10.6.39: Polar equations of conics can be used to describe the motion of com...
 10.10.6.40: Polar equations of conics can be used to describe the motion of com...
 10.10.6.41: Polar equations of conics can be used to describe the motion of com...
 10.10.6.42: Polar equations of conics can be used to describe the motion of com...
 10.10.6.43: Earths orbit The closest Earth gets to the sun is about 91,405,950 ...
 10.10.7.1: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.2: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.3: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.4: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.5: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.6: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.7: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.8: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.9: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.10: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.11: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.12: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.13: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.14: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.15: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.16: Find the vertices and foci of the conic, and sketch its graph.
 10.10.7.17: Find the standard equation of a parabola with a vertical axis that ...
 10.10.7.18: Find the standard equation of a parabola with a vertical axis that ...
 10.10.7.19: Find an equation for the conic that satisfies the given conditions....
 10.10.7.20: Find an equation for the conic that satisfies the given conditions....
 10.10.7.21: Find an equation for the conic that satisfies the given conditions....
 10.10.7.22: Find an equation for the conic that satisfies the given conditions....
 10.10.7.23: Find an equation for the conic that satisfies the given conditions....
 10.10.7.24: Find an equation for the conic that satisfies the given conditions....
 10.10.7.25: Find an equation for the conic that satisfies the given conditions....
 10.10.7.26: Find an equation for the conic that satisfies the given conditions....
 10.10.7.27: Find an equation for the conic that satisfies the given conditions....
 10.10.7.28: Find an equation for the conic that satisfies the given conditions....
 10.10.7.29: Find an equation for the portion of the conic.Right half of
 10.10.7.30: Find an equation for the portion of the conic.Lower half of
 10.10.7.31: Find an equation for the portion of the conic. Left half of
 10.10.7.32: Find an equation for the portion of the conic.Upper half of
 10.10.7.33: Find an equation for the portion of the conic. Right branch of
 10.10.7.34: Find an equation for the portion of the conic.Lower branch of
 10.10.7.35: (a) Determine A so that the point is on the conic .(b) Is the conic...
 10.10.7.36: If a square with sides parallel to the coordinate axes is inscribed...
 10.10.7.37: Find the standard equation of the circle that has center at the foc...
 10.10.7.38: Focal length and angular velocity A cylindrical container, partiall...
 10.10.7.39: An ellipse has a vertex at the origin and foci and , as shown in th...
 10.10.7.40: Alpha particles In 1911, the physicist Ernest Rutherford (18711937)...
 10.10.7.41: Find an equation in x and y whose graph contains the points on the ...
 10.10.7.42: Find an equation in x and y whose graph contains the points on the ...
 10.10.7.43: Find an equation in x and y whose graph contains the points on the ...
 10.10.7.44: Find an equation in x and y whose graph contains the points on the ...
 10.10.7.45: Find an equation in x and y whose graph contains the points on the ...
 10.10.7.46: Curves , , , and are given parametrically for t in . Sketch their g...
 10.10.7.47: Refer to the equations in (1) of Example 6 in Section 10.4. Find th...
 10.10.7.48: List two polar coordinate points that represent the same point as .
 10.10.7.49: Change to rectangular coordinates.
 10.10.7.50: Change to polar coordinates with and .
 10.10.7.51: Find a polar equation that has the same graph as the equation in x ...
 10.10.7.52: Find a polar equation that has the same graph as the equation in x ...
 10.10.7.53: Find a polar equation that has the same graph as the equation in x ...
 10.10.7.54: Find a polar equation that has the same graph as the equation in x ...
 10.10.7.55: Find an equation in x and y that has the same graph as the polar eq...
 10.10.7.56: Find an equation in x and y that has the same graph as the polar eq...
 10.10.7.57: Find an equation in x and y that has the same graph as the polar eq...
 10.10.7.58: Find an equation in x and y that has the same graph as the polar eq...
 10.10.7.59: Find an equation in x and y that has the same graph as the polar eq...
 10.10.7.60: Find an equation in x and y that has the same graph as the polar eq...
 10.10.7.61: Sketch the graph of the polar equation.
 10.10.7.62: Sketch the graph of the polar equation.
 10.10.7.63: Sketch the graph of the polar equation.
 10.10.7.64: Sketch the graph of the polar equation.
 10.10.7.65: Sketch the graph of the polar equation.
 10.10.7.66: Sketch the graph of the polar equation.
 10.10.7.67: Sketch the graph of the polar equation.
 10.10.7.68: Sketch the graph of the polar equation.
 10.10.7.69: Sketch the graph of the polar equation.
 10.10.7.70: Sketch the graph of the polar equation.
 10.10.7.71: Sketch the graph of the polar equation.
 10.10.7.72: Sketch the graph of the polar equation.
 10.10.8.1: On a parabola, the line segment through the focus, perpendicular to...
 10.10.8.2: On the graph of a hyperbola with center at the origin O, draw a cir...
 10.10.8.3: A point is on an ellipse if and only ifIf , derive the general equa...
 10.10.8.4: A point is on a hyperbola if and only ifIf , derive the general equ...
 10.10.8.5: A point is the same distance from as it is from the circle , as ill...
 10.10.8.6: Design of a telescope Refer to Exercise 78 in Section 10.3. Suppose...
 10.10.8.7: Maximizing a projectiles range As in Example 6 in Section 10.4, sup...
 10.10.8.8: Generalizations for a projectiles path If , the equations in (1) of...
 10.10.8.9: Investigating a Lissajous figure Find an equation in x and y for th...
 10.10.8.10: Sketch the graphs of the equations , , and for . Try as many values...
 10.10.8.11: Generalized roses Examine the graph of for odd values of n and even...
 10.10.8.12: Figure 17 of Section 10.5 shows the circles and . Solve this system...
 10.10.9.1: Sketch the graph of the parabola . Label its vertex, focus, and dir...
 10.10.9.2: Find an equation for the parabola shown in the figure.
 10.10.9.3: Find an equation of the parabola that has vertex and the xaxis as ...
 10.10.9.4: Find an equation for the lower half of the parabola .
 10.10.9.5: Find an equation for the parabola that has a horizontal axis and pa...
 10.10.9.6: A searchlight reflector has the shape of a paraboloid, with the lig...
 10.10.9.7: Sketch the graph of the ellipse . Label its vertices, foci, and end...
 10.10.9.8: Find an equation for the ellipse that has its center at the origin,...
 10.10.9.9: An ellipse has vertices and minor axis length 8. Find its eccentric...
 10.10.9.10: Find an equation for the set of points in an xyplane such that the...
 10.10.9.11: Find an equation for the left half of the ellipse .
 10.10.9.12: An arch of a bridge is semielliptical, with major axis horizontal....
 10.10.9.13: Sketch the graph of the hyperbola . Label its vertices, foci, and a...
 10.10.9.14: Given that a hyperbola has vertices and foci , find equations of th...
 10.10.9.15: Find an equation for the hyperbola that has its center at the origi...
 10.10.9.16: Find an equation for the left branch of the hyperbola .
 10.10.9.17: Find an equation in x and y whose graph contains the points on the ...
 10.10.9.18: Find an equation in x and y whose graph contains the points on the ...
 10.10.9.19: Write a parametrization for the bottom branch of .
 10.10.9.20: Describe the graph (and orientation for increasing values of t) of ...
 10.10.9.21: Suppose a projectile is fired at a speed of 544 ftsec at an angle o...
 10.10.9.22: Change the rectangular coordinates to polar coordinates with and .
 10.10.9.23: Find a polar equation that has the same graph as .
 10.10.9.24: Find an equation in x and y that has the same graph as .
 10.10.9.25: Sketch the graph of .
 10.10.9.26: Sketch the graph of .
 10.10.9.27: Find the eccentricity of . Classify the conic, sketch the graph, an...
 10.10.9.28: Find an equation in x and y for .
 10.10.9.29: Find a polar equation of the conic with focus at the pole that has ...
Solutions for Chapter 10: TOPICS FROM ANALYTIC GEOMETRY
Full solutions for Precalculus: Functions and Graphs  12th Edition
ISBN: 9780840068576
Solutions for Chapter 10: TOPICS FROM ANALYTIC GEOMETRY
Get Full SolutionsPrecalculus: Functions and Graphs was written by and is associated to the ISBN: 9780840068576. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus: Functions and Graphs, edition: 12. Since 547 problems in chapter 10: TOPICS FROM ANALYTIC GEOMETRY have been answered, more than 19163 students have viewed full stepbystep solutions from this chapter. Chapter 10: TOPICS FROM ANALYTIC GEOMETRY includes 547 full stepbystep solutions.

Additive inverse of a complex number
The opposite of a + bi, or a  bi

Angle
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)

Arithmetic sequence
A sequence {an} in which an = an1 + d for every integer n ? 2 . The number d is the common difference.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Components of a vector
See Component form of a vector.

Constant of variation
See Power function.

Constraints
See Linear programming problem.

Deductive reasoning
The process of utilizing general information to prove a specific hypothesis

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

Equilibrium point
A point where the supply curve and demand curve intersect. The corresponding price is the equilibrium price.

Independent variable
Variable representing the domain value of a function (usually x).

Inverse sine function
The function y = sin1 x

Inverse variation
See Power function.

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Partial fraction decomposition
See Partial fractions.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Sine
The function y = sin x.

Variable (in statistics)
A characteristic of individuals that is being identified or measured.

Vector
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.