 10.10.1: Sketch and identify the curve defined by the parametric equations x...
 10.10.2: What curve is represented by the following parametric equations?x c...
 10.10.3: What curve is represented by the given parametric equations?x sin 2...
 10.10.4: Find parametric equations for the circle with center and radius r
 10.10.5: Sketch the curve with parametric equations x sin t ,y sin2 t
 10.10.6: Use a graphing device to graph the curve x y 4 3y 2
 10.10.7: The curve traced out by a point on the circumference of a circle as...
 10.10.8: Investigate the family of curves with parametric equations What do ...
 10.10.9: Sketch the curve by using the parametric equations to plot x 1 3t p...
 10.10.10: Sketch the curve by using the parametric equations to plot x 1 3t p...
 10.10.11: Sketch the curve by using the parametric equations to plot x 1 3t p...
 10.10.12: Sketch the curve by using the parametric equations to plot x 1 3t p...
 10.10.13: Sketch the curve by using the parametric equations to plot points. ...
 10.10.14: Sketch the curve by using the parametric equations to plot points. ...
 10.10.15: Sketch the curve by using the parametric equations to plot points. ...
 10.10.16: Sketch the curve by using the parametric equations to plot points. ...
 10.10.17: Sketch the curve by using the parametric equations to plot points. ...
 10.10.18: Sketch the curve by using the parametric equations to plot points. ...
 10.10.19: a) Eliminate the parameter to find a Cartesian equation of the curv...
 10.10.20: a) Eliminate the parameter to find a Cartesian equation of the curv...
 10.10.21: a) Eliminate the parameter to find a Cartesian equation of the curv...
 10.10.22: a) Eliminate the parameter to find a Cartesian equation of the curv...
 10.10.23: a) Eliminate the parameter to find a Cartesian equation of the curv...
 10.10.24: a) Eliminate the parameter to find a Cartesian equation of the curv...
 10.10.25: a) Eliminate the parameter to find a Cartesian equation of the curv...
 10.10.26: a) Eliminate the parameter to find a Cartesian equation of the curv...
 10.10.27: Describe the motion of a particle with position as varies in the gi...
 10.10.28: Describe the motion of a particle with position as varies in the gi...
 10.10.29: Describe the motion of a particle with position as varies in the gi...
 10.10.30: Describe the motion of a particle with position as varies in the gi...
 10.10.31: Suppose a curve is given by the parametric equations , , where the ...
 10.10.32: Match the graphs of the parametric equations and in (a)(d) with the...
 10.10.33: Use the graphs of and to sketch the parametric curve , . Indicate w...
 10.10.34: Use the graphs of and to sketch the parametric curve , . Indicate w...
 10.10.35: Use the graphs of and to sketch the parametric curve , . Indicate w...
 10.10.36: Match the parametric equations with the graphs labeled IVI. Give r...
 10.10.37: Graph the curve x y 3y 3 y 5 x
 10.10.38: Graph the curves and and find their points of intersection correct ...
 10.10.39: (a) Show that the parametric equations 41. ba where , describe the ...
 10.10.40: Use a graphing device and the result of Exercise 31(a) to draw the ...
 10.10.41: Find parametric equations for the path of a particle that moves alo...
 10.10.42: (a) Find parametric equations for the ellipse . [Hint: Modify the e...
 10.10.43: Use a graphing calculator or computer to reproduce the picture.
 10.10.44: Compare the curves represented by the parametric equations. How do ...
 10.10.45: Compare the curves represented by the parametric equations. How do ...
 10.10.46: Derive Equations 1 for the case 2
 10.10.47: Let be a point at a distance from the center of a circle of radius ...
 10.10.48: If and are fixed numbers, find parametric equations for the curve t...
 10.10.49: If and are fixed numbers, find parametric equations for the curve t...
 10.10.50: A curve, called a witch of Maria Agnesi, consists of all possible p...
 10.10.51: a) Find parametric equations for the set of all points as shown in ...
 10.10.52: Suppose that the position of one particle at time is given by and t...
 10.10.53: If a projectile is fired with an initial velocity of meters per sec...
 10.10.54: Investigate the family of curves defined by the parametric equation...
 10.10.55: The swallowtail catastrophe curves are defined by the parametric eq...
 10.10.56: The curves with equations , are called Lissajous figures. Investiga...
 10.10.57: Investigate the family of curves defined by the parametric equation...
 10.10.58: A curve is defined by the parametric equations , (a) Show that has ...
 10.10.59: (a) Find the tangent to the cycloid , at the point where . (See Exa...
 10.10.60: Find the area under one arch of the cycloid x rsin y r1 cos V or
 10.10.61: If we use the representation of the unit circle given in Example 2 ...
 10.10.62: Find the length of one arch of the cycloid
 10.10.63: Show that the surface area of a sphere of radius is 4 r 2
 10.10.64: Find an equation of the tangent to the curve at the point correspon...
 10.10.65: Find an equation of the tangent to the curve at the point correspon...
 10.10.66: Find an equation of the tangent to the curve at the point correspon...
 10.10.67: Find an equation of the tangent to the curve at the point correspon...
 10.10.68: Find an equation of the tangent to the curve at the given point by ...
 10.10.69: Find an equation of the tangent to the curve at the given point by ...
 10.10.70: Find an equation of the tangent(s) to the curve at the given point....
 10.10.71: Find an equation of the tangent(s) to the curve at the given point....
 10.10.72: Find and . For which values of is the curve concave upward?
 10.10.73: Find and . For which values of is the curve concave upward?
 10.10.74: Find and . For which values of is the curve concave upward?
 10.10.75: Find and . For which values of is the curve concave upward?
 10.10.76: Find and . For which values of is the curve concave upward?
 10.10.77: Find and . For which values of is the curve concave upward?
 10.10.78: Find the points on the curve where the tangent is horizontal or ver...
 10.10.79: Find the points on the curve where the tangent is horizontal or ver...
 10.10.80: Find the points on the curve where the tangent is horizontal or ver...
 10.10.81: Find the points on the curve where the tangent is horizontal or ver...
 10.10.82: Use a graph to estimate the coordinates of the rightmost point on t...
 10.10.83: Use a graph to estimate the coordinates of the lowest point and the...
 10.10.84: Graph the curve in a viewing rectangle that displays all the import...
 10.10.85: Graph the curve in a viewing rectangle that displays all the import...
 10.10.86: Show that the curve , has two tangents at and find their equations....
 10.10.87: Graph the curve , to discover where it crosses itself. Then find eq...
 10.10.88: a) Find the slope of the tangent line to the trochoid , in terms of...
 10.10.89: a) Find the slope of the tangent to the astroid , in terms of . (As...
 10.10.90: At what points on the curve , does the tangent line have slope ?
 10.10.91: Find equations of the tangents to the curve , that pass through the...
 10.10.92: Use the parametric equations of an ellipse, , y b sin , 0 2, to fin...
 10.10.93: Find the area enclosed by the curve , and n 6 the yaxis
 10.10.94: Find the area enclosed by the and the curve
 10.10.95: Find the area of the region enclosed by the astroid , . (Astroids a...
 10.10.96: Find the area under one arch of the trochoid of Exercise 40 in Sect...
 10.10.97: Let be the region enclosed by the loop of the curve in Example 1. (...
 10.10.98: Set up an integral that represents the length of the curve. Then us...
 10.10.99: Set up an integral that represents the length of the curve. Then us...
 10.10.100: Set up an integral that represents the length of the curve. Then us...
 10.10.101: Set up an integral that represents the length of the curve. Then us...
 10.10.102: Find the exact length of the curve
 10.10.103: Find the exact length of the curve
 10.10.104: Find the exact length of the curve
 10.10.105: Find the exact length of the curve
 10.10.106: Graph the curve and find its length.
 10.10.107: Graph the curve and find its length.
 10.10.108: Graph the curve and find its length.
 10.10.109: Find the length of the loop of the curve , y 3t .
 10.10.110: Use Simpsons Rule with to estimate the length of the curve y t e 6 ...
 10.10.111: In Exercise 43 in Section 10.1 you were asked to derive the paramet...
 10.10.112: Find the distance traveled by a particle with position as varies in...
 10.10.113: Find the distance traveled by a particle with position as varies in...
 10.10.114: Show that the total length of the ellipse (e ca , is where c sa2 b2...
 10.10.115: Find the total length of the astroid , , where a>0
 10.10.116: (a) Graph the epitrochoid with equations What parameter interval gi...
 10.10.117: A curve called Cornus spiral is defined by the parametric equations...
 10.10.118: Set up an integral that represents the area of the surface obtained...
 10.10.119: Set up an integral that represents the area of the surface obtained...
 10.10.120: Find the exact area of the surface obtained by rotating the y fx gi...
 10.10.121: Find the exact area of the surface obtained by rotating the y fx gi...
 10.10.122: Find the exact area of the surface obtained by rotating the y fx gi...
 10.10.123: Graph the curve If this curve is rotated about the axis, find the ...
 10.10.124: If the curve is rotated about the axis, use your calculator to est...
 10.10.125: If the arc of the curve in Exercise 50 is rotated about the axis, ...
 10.10.126: Find the surface area generated by rotating the given curve about t...
 10.10.127: Find the surface area generated by rotating the given curve about t...
 10.10.128: If is continuous and for , show that the parametric curve , , , can...
 10.10.129: Use Formula 2 to derive Formula 7 from Formula 8.2.5 for the case i...
 10.10.130: The curvature at a point of a curve is defined as where is the angl...
 10.10.131: a) Use the formula in Exercise 69(b) to find the curvature of the p...
 10.10.132: Use the formula in Exercise 69(a) to find the curvature of the cycl...
 10.10.133: a) Show that the curvature at each point of a straight line is . (b...
 10.10.134: A string is wound around a circle and then unwound while being held...
 10.10.135: A cow is tied to a silo with radius by a rope just long enough to r...
 10.10.136: Plot the points whose polar coordinates are given. (a) (b) (c) (d)
 10.10.137: Convert the point from polar to Cartesian coordinates.
 10.10.138: Represent the point with Cartesian coordinates in terms of polar co...
 10.10.139: What curve is represented by the polar equation r=2?
 10.10.140: Sketch the polar curve 0=1
 10.10.141: (a) Sketch the curve with polar equation . (b) Find a Cartesian equ...
 10.10.142: Sketch the curve r 1 sin
 10.10.143: Sketch the curve r cos 2
 10.10.144: a) For the cardioid of Example 7, find the slope of the tangent lin...
 10.10.145: Graph the curve r sin85 t
 10.10.146: Investigate the family of polar curves given by . How does the shap...
 10.10.147: Plot the point whose polar coordinates are given. Then find (s2 , 5...
 10.10.148: Plot the point whose polar coordinates are given. Then find (s2 , 5...
 10.10.149: Plot the point whose polar coordinates are given. Then find the Car...
 10.10.150: Plot the point whose polar coordinates are given. Then find the Car...
 10.10.151: The Cartesian coordinates of a point are given. (i) Find polar coor...
 10.10.152: The Cartesian coordinates of a point are given. (i) Find polar coor...
 10.10.153: Sketch the region in the plane consisting of points whose polar coo...
 10.10.154: Sketch the region in the plane consisting of points whose polar coo...
 10.10.155: Sketch the region in the plane consisting of points whose polar coo...
 10.10.156: Sketch the region in the plane consisting of points whose polar coo...
 10.10.157: Sketch the region in the plane consisting of points whose polar coo...
 10.10.158: Sketch the region in the plane consisting of points whose polar coo...
 10.10.159: Find the distance between the points with polar coordinates and
 10.10.160: Find a formula for the distance between the points with polar coord...
 10.10.161: Identify the curve by finding a Cartesian equation for the curver 2
 10.10.162: Identify the curve by finding a Cartesian equation for the curver c...
 10.10.163: Identify the curve by finding a Cartesian equation for the curver 3...
 10.10.164: Identify the curve by finding a Cartesian equation for the curver 2...
 10.10.165: Identify the curve by finding a Cartesian equation for the curver c...
 10.10.166: Identify the curve by finding a Cartesian equation for the curver t...
 10.10.167: Find a polar equation for the curve represented by the given Cartes...
 10.10.168: Find a polar equation for the curve represented by the given Cartes...
 10.10.169: Find a polar equation for the curve represented by the given Cartes...
 10.10.170: Find a polar equation for the curve represented by the given Cartes...
 10.10.171: Find a polar equation for the curve represented by the given Cartes...
 10.10.172: Find a polar equation for the curve represented by the given Cartes...
 10.10.173: For each of the described curves, decide if the curve would be more...
 10.10.174: For each of the described curves, decide if the curve would be more...
 10.10.175: Sketch the curve with the given polar equation6 2
 10.10.176: Sketch the curve with the given polar equationr 6 2 3r 2 0 2,
 10.10.177: Sketch the curve with the given polar equationr sin r
 10.10.178: Sketch the curve with the given polar equationr 3 cos
 10.10.179: Sketch the curve with the given polar equationr 21 sin 0 r 1
 10.10.180: Sketch the curve with the given polar equationr 1 3 cos
 10.10.181: Sketch the curve with the given polar equationr 0 r
 10.10.182: Sketch the curve with the given polar equationr ln 1 r
 10.10.183: Sketch the curve with the given polar equationr 4 sin 3r
 10.10.184: Sketch the curve with the given polar equationr cos 5
 10.10.185: Sketch the curve with the given polar equationr 2 cos 4r
 10.10.186: Sketch the curve with the given polar equationr 3 cos 6
 10.10.187: Sketch the curve with the given polar equationr 1 2 sin 4
 10.10.188: Sketch the curve with the given polar equationr 2 sin
 10.10.189: Sketch the curve with the given polar equation
 10.10.190: Sketch the curve with the given polar equation
 10.10.191: Sketch the curve with the given polar equation
 10.10.192: Sketch the curve with the given polar equation
 10.10.193: Sketch the curve with the given polar equation
 10.10.194: Sketch the curve with the given polar equation
 10.10.195: The figure shows the graph of as a function of in Cartesian coordin...
 10.10.196: The figure shows the graph of as a function of in Cartesian coordin...
 10.10.197: Show that the polar curve (called a conchoid) has the line as a ver...
 10.10.198: Show that the curve (also a conchoid) has the line as a horizontal ...
 10.10.199: Show that the curve (called a cissoid of Diocles) has the line as a...
 10.10.200: Sketch the curve x 2 y 2 3 4x 2 y 2
 10.10.201: a) In Example 11 the graphs suggest that the limaon has an inner lo...
 10.10.202: Match the polar equations with the graphs labeled IVI. Give reasons...
 10.10.203: Find the slope of the tangent line to the given polar curve at the ...
 10.10.204: Find the slope of the tangent line to the given polar curve at the ...
 10.10.205: Find the slope of the tangent line to the given polar curve at the ...
 10.10.206: Find the slope of the tangent line to the given polar curve at the ...
 10.10.207: Find the slope of the tangent line to the given polar curve at the ...
 10.10.208: Find the slope of the tangent line to the given polar curve at the ...
 10.10.209: Find the points on the given curve where the tangent line is horizo...
 10.10.210: Find the points on the given curve where the tangent line is horizo...
 10.10.211: Find the points on the given curve where the tangent line is horizo...
 10.10.212: Find the points on the given curve where the tangent line is horizo...
 10.10.213: Find the points on the given curve where the tangent line is horizo...
 10.10.214: Find the points on the given curve where the tangent line is horizo...
 10.10.215: Show that the polar equation , where , represents a circle, and fin...
 10.10.216: Show that the curves and intersect at right angles.
 10.10.217: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.218: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.219: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.220: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.221: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.222: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.223: How are the graphs of and related to the graph of ? In general, how...
 10.10.224: Use a graph to estimate the coordinate of the highest points on th...
 10.10.225: (a) Investigate the family of curves defined by the polar equations...
 10.10.226: A family of curves is given by the equations , where is a real numb...
 10.10.227: A family of curves has polar equations Investigate how the graph ch...
 10.10.228: The astronomer Giovanni Cassini (16251712) studied the family of cu...
 10.10.229: Let be any point (except the origin) on the curve . If is the angle...
 10.10.230: a) Use Exercise 83 to show that the angle between the tangent line ...
 10.10.231: Find the area of the region that is bounded by the given curve r 3 ...
 10.10.232: Find the area of the region that is bounded by the given curve r 3 ...
 10.10.233: Find the area of the region that is bounded by the given curve r 3 ...
 10.10.234: Find the area of the region that is bounded by the given curve r 3 ...
 10.10.235: Find the area of the shaded region
 10.10.236: Find the area of the shaded region
 10.10.237: Find the area of the shaded region
 10.10.238: Find the area of the shaded region
 10.10.239: Sketch the curve and find the area that it encloses.r 3 cos r
 10.10.240: Sketch the curve and find the area that it encloses.r 3 cos r
 10.10.241: Sketch the curve and find the area that it encloses.r r 2 sin 11. 2...
 10.10.242: Sketch the curve and find the area that it encloses.r r 2 sin 11. 2...
 10.10.243: Sketch the curve and find the area that it encloses.r 2 cos 3r
 10.10.244: Sketch the curve and find the area that it encloses.r 2 cos 2
 10.10.245: Graph the curve and find the area that it encloses
 10.10.246: Graph the curve and find the area that it encloses
 10.10.247: Find the area of the region enclosed by one loop of the curve r sin...
 10.10.248: Find the area of the region enclosed by one loop of the curve r 4 s...
 10.10.249: Find the area of the region enclosed by one loop of the curve r 3 c...
 10.10.250: Find the area of the region enclosed by one loop of the curve r 2 s...
 10.10.251: Find the area of the region enclosed by one loop of the curve r 1 2...
 10.10.252: Find the area enclosed by the loop of the strophoid r 2 cos sec 2
 10.10.253: Find the area of the region that lies inside the first curve and ou...
 10.10.254: Find the area of the region that lies inside the first curve and ou...
 10.10.255: Find the area of the region that lies inside the first curve and ou...
 10.10.256: Find the area of the region that lies inside the first curve and ou...
 10.10.257: Find the area of the region that lies inside the first curve and ou...
 10.10.258: Find the area of the region that lies inside the first curve and ou...
 10.10.259: Find the area of the region that lies inside both curves.
 10.10.260: Find the area of the region that lies inside both curves.
 10.10.261: Find the area of the region that lies inside both curves.
 10.10.262: Find the area of the region that lies inside both curves.
 10.10.263: Find the area of the region that lies inside both curves.
 10.10.264: Find the area of the region that lies inside both curves.r a sin r ...
 10.10.265: Find the area inside the larger loop and outside the smaller loop o...
 10.10.266: Find the area between a large loop and the enclosed small loop of t...
 10.10.267: Find all points of intersection of the given curves.
 10.10.268: Find all points of intersection of the given curves.
 10.10.269: Find all points of intersection of the given curves.
 10.10.270: Find all points of intersection of the given curves.
 10.10.271: Find all points of intersection of the given curves.
 10.10.272: Find all points of intersection of the given curves.
 10.10.273: The points of intersection of the cardioid and the spiral loop , , ...
 10.10.274: When recording live performances, sound engineers often use a micro...
 10.10.275: Find the exact length of the polar curve.
 10.10.276: Find the exact length of the polar curve.
 10.10.277: Find the exact length of the polar curve.
 10.10.278: Find the exact length of the polar curve.
 10.10.279: Use a calculator to find the length of the curve correct to four de...
 10.10.280: Use a calculator to find the length of the curve correct to four de...
 10.10.281: Use a calculator to find the length of the curve correct to four de...
 10.10.282: Use a calculator to find the length of the curve correct to four de...
 10.10.283: Graph the curve and find its length
 10.10.284: Graph the curve and find its length
 10.10.285: a) Use Formula 10.2.7 to show that the area of the surface generate...
 10.10.286: (a) Find a formula for the area of the surface generated by rotatin...
 10.10.287: Find the focus and directrix of the parabola and sketch the graph
 10.10.288: Sketch the graph of and locate the foci.
 10.10.289: Find an equation of the ellipse with foci and vertices 0, 3
 10.10.290: Find the foci and asymptotes of the hyperbola and sketch its graph
 10.10.291: Find the foci and equation of the hyperbola with vertices and asymp...
 10.10.292: Find an equation of the ellipse with foci , and vertices 1, 25, 2 2,
 10.10.293: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.294: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.295: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.296: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.297: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.298: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.299: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.300: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.301: Find an equation of the parabola. Then find the focus and directrix
 10.10.302: Find an equation of the parabola. Then find the focus and directrix
 10.10.303: Find the vertices and foci of the ellipse and sketch its graphx 2 9...
 10.10.304: Find the vertices and foci of the ellipse and sketch its graphx 2 6...
 10.10.305: Find the vertices and foci of the ellipse and sketch its graph4x 2 ...
 10.10.306: Find the vertices and foci of the ellipse and sketch its graph4x 2 ...
 10.10.307: Find the vertices and foci of the ellipse and sketch its graph9x 2 ...
 10.10.308: Find the vertices and foci of the ellipse and sketch its graphx 2 3...
 10.10.309: Find an equation of the ellipse. Then find its foci
 10.10.310: Find an equation of the ellipse. Then find its foci
 10.10.311: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.312: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.313: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.314: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.315: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.316: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.317: Identify the type of conic section whose equation is given and find...
 10.10.318: Identify the type of conic section whose equation is given and find...
 10.10.319: Identify the type of conic section whose equation is given and find...
 10.10.320: Identify the type of conic section whose equation is given and find...
 10.10.321: Identify the type of conic section whose equation is given and find...
 10.10.322: Identify the type of conic section whose equation is given and find...
 10.10.323: Find an equation for the conic that satisfies the given conditions.
 10.10.324: Find an equation for the conic that satisfies the given conditions.
 10.10.325: Find an equation for the conic that satisfies the given conditions.
 10.10.326: Find an equation for the conic that satisfies the given conditions.
 10.10.327: Find an equation for the conic that satisfies the given conditions.
 10.10.328: Find an equation for the conic that satisfies the given conditions.
 10.10.329: Find an equation for the conic that satisfies the given conditions.
 10.10.330: Find an equation for the conic that satisfies the given conditions.
 10.10.331: Find an equation for the conic that satisfies the given conditions.
 10.10.332: Find an equation for the conic that satisfies the given conditions.
 10.10.333: Find an equation for the conic that satisfies the given conditions.
 10.10.334: Find an equation for the conic that satisfies the given conditions.
 10.10.335: Find an equation for the conic that satisfies the given conditions.
 10.10.336: Find an equation for the conic that satisfies the given conditions.
 10.10.337: Find an equation for the conic that satisfies the given conditions.
 10.10.338: Find an equation for the conic that satisfies the given conditions.
 10.10.339: Find an equation for the conic that satisfies the given conditions.
 10.10.340: Find an equation for the conic that satisfies the given conditions.
 10.10.341: The point in a lunar orbit nearest the surface of the moon is calle...
 10.10.342: A crosssection of a parabolic reflector is shown in the figure. Th...
 10.10.343: In the LORAN (LOng RAnge Navigation) radio navigation system, two r...
 10.10.344: Use the definition of a hyperbola to derive Equation 6 for a hyperb...
 10.10.345: Show that the function defined by the upper branch of the hyperbola...
 10.10.346: Find an equation for the ellipse with foci and and major axis of le...
 10.10.347: Determine the type of curve represented by the equation in each of ...
 10.10.348: (a) Show that the equation of the tangent line to the parabola at t...
 10.10.349: Show that the tangent lines to the parabola drawn from any point on...
 10.10.350: Show that if an ellipse and a hyperbola have the same foci, then th...
 10.10.351: Use Simpsons Rule with to estimate the length of the ellipse x 2 4y...
 10.10.352: The planet Pluto travels in an elliptical orbit around the sun (at ...
 10.10.353: Find the area of the region enclosed by the hyperbola and the verti...
 10.10.354: (a) If an ellipse is rotated about its major axis, find the volume ...
 10.10.355: Let be a point on the ellipse with foci and and let and be the angl...
 10.10.356: Let be a point on the hyperbola with foci and and let and be the an...
 10.10.357: Find a polar equation for a parabola that has its focus at the orig...
 10.10.358: A conic is given by the polar equation Find the eccentricity, ident...
 10.10.359: Sketch the conic r 12 2 4 sin
 10.10.360: If the ellipse of Example 2 is rotated through an angle about the o...
 10.10.361: a) Find an approximate polar equation for the elliptical orbit of t...
 10.10.362: Write a polar equation of a conic with the focus at the origin and ...
 10.10.363: Write a polar equation of a conic with the focus at the origin and ...
 10.10.364: Write a polar equation of a conic with the focus at the origin and ...
 10.10.365: Write a polar equation of a conic with the focus at the origin and ...
 10.10.366: Write a polar equation of a conic with the focus at the origin and ...
 10.10.367: Write a polar equation of a conic with the focus at the origin and ...
 10.10.368: Write a polar equation of a conic with the focus at the origin and ...
 10.10.369: Write a polar equation of a conic with the focus at the origin and ...
 10.10.370: a) Find the eccentricity, (b) identify the conic, (c) give an equat...
 10.10.371: a) Find the eccentricity, (b) identify the conic, (c) give an equat...
 10.10.372: a) Find the eccentricity, (b) identify the conic, (c) give an equat...
 10.10.373: a) Find the eccentricity, (b) identify the conic, (c) give an equat...
 10.10.374: a) Find the eccentricity, (b) identify the conic, (c) give an equat...
 10.10.375: a) Find the eccentricity, (b) identify the conic, (c) give an equat...
 10.10.376: a) Find the eccentricity, (b) identify the conic, (c) give an equat...
 10.10.377: a) Find the eccentricity, (b) identify the conic, (c) give an equat...
 10.10.378: (a) Find the eccentricity and directrix of the conic and graph the ...
 10.10.379: Graph the conic and its directrix. Also graph the conic obtained by...
 10.10.380: Graph the conics with , , , and on a common screen. How does the va...
 10.10.381: (a) Graph the conics for and various values of . How does the value...
 10.10.382: Show that a conic with focus at the origin, eccentricity , and dire...
 10.10.383: Show that a conic with focus at the origin, eccentricity , and dire...
 10.10.384: Show that a conic with focus at the origin, eccentricity , and dire...
 10.10.385: Show that the parabolas and intersect at right angles.
 10.10.386: The orbit of Mars around the sun is an ellipse with eccentricity an...
 10.10.387: Jupiters orbit has eccentricity and the length of the major axis is...
 10.10.388: The orbit of Halleys comet, last seen in 1986 and due to return in ...
 10.10.389: The HaleBopp comet, discovered in 1995, has an elliptical orbit wi...
 10.10.390: The planet Mercury travels in an elliptical orbit with eccentricity...
 10.10.391: The distance from the planet Pluto to the sun is km at perihelion a...
 10.10.392: Using the data from Exercise 29, find the distance traveled by the ...
 10.10.393: a) What is a parametric curve? (b) How do you sketch a parametric c...
 10.10.394: a) How do you find the slope of a tangent to a parametric curve? (b...
 10.10.395: Write an expression for each of the following: (a) The length of a ...
 10.10.396: a) Use a diagram to explain the meaning of the polar coordinates of...
 10.10.397: (a) How do you find the slope of a tangent line to a polar curve? (...
 10.10.398: (a) Give a geometric definition of a parabola. (b) Write an equatio...
 10.10.399: (a) Give a definition of an ellipse in terms of foci. (b) Write an ...
 10.10.400: a) Give a definition of a hyperbola in terms of foci. (b) Write an ...
 10.10.401: a) What is the eccentricity of a conic section? (b) What can you sa...
 10.10.402: Determine whether the statement is true or false. If it is true, ex...
 10.10.403: Determine whether the statement is true or false. If it is true, ex...
 10.10.404: Determine whether the statement is true or false. If it is true, ex...
 10.10.405: Determine whether the statement is true or false. If it is true, ex...
 10.10.406: Determine whether the statement is true or false. If it is true, ex...
 10.10.407: Determine whether the statement is true or false. If it is true, ex...
 10.10.408: Determine whether the statement is true or false. If it is true, ex...
 10.10.409: Determine whether the statement is true or false. If it is true, ex...
 10.10.410: Determine whether the statement is true or false. If it is true, ex...
 10.10.411: Determine whether the statement is true or false. If it is true, ex...
 10.10.412: Sketch the parametric curve and eliminate the parameter to find the...
 10.10.413: Sketch the parametric curve and eliminate the parameter to find the...
 10.10.414: Sketch the parametric curve and eliminate the parameter to find the...
 10.10.415: Sketch the parametric curve and eliminate the parameter to find the...
 10.10.416: Write three different sets of parametric equations for the curve y sx
 10.10.417: Use the graphs of and to sketch the parametric curve , . Indicate w...
 10.10.418: a) Plot the point with polar coordinates . Then find its Cartesian ...
 10.10.419: Sketch the region consisting of points whose polar coordinates sati...
 10.10.420: Sketch the polar curver 1 cos r
 10.10.421: Sketch the polar curve]r sin 4
 10.10.422: Sketch the polar curver cos 3 r
 10.10.423: Sketch the polar curver 3 cos 3
 10.10.424: Sketch the polar curver 1 cos 2 r
 10.10.425: Sketch the polar curver 2 cos 2 r
 10.10.426: Sketch the polar curver 3 1 2 sin
 10.10.427: Sketch the polar curver 3 2 2 cos r
 10.10.428: Find a polar equation for the curve represented by the given Cartes...
 10.10.429: Find a polar equation for the curve represented by the given Cartes...
 10.10.430: The curve with polar equation is called a cochleoid. Use a graph of...
 10.10.431: Graph the ellipse and its directrix. Also graph the ellipse obtaine...
 10.10.432: Find the slope of the tangent line to the given curve at the point ...
 10.10.433: Find the slope of the tangent line to the given curve at the point ...
 10.10.434: Find the slope of the tangent line to the given curve at the point ...
 10.10.435: Find the slope of the tangent line to the given curve at the point ...
 10.10.436: Use a graph to estimate the coordinates of the lowest point on the ...
 10.10.437: Find the area enclosed by the loop of the curve in Exercise 27.
 10.10.438: At what points does the curve have vertical or horizontal tangents?...
 10.10.439: Find the area enclosed by the curve in Exercise 29
 10.10.440: Find the area enclosed by the curve r 2 9 cos 5
 10.10.441: Find the area enclosed by the inner loop of the curve r 1 3 sin
 10.10.442: Find the points of intersection of the curves and r 4 cos
 10.10.443: Find the points of intersection of the curves r 2 cos r
 10.10.444: Find the area of the region that lies inside both of the circles r ...
 10.10.445: Find the area of the region that lies inside the curve but outside ...
 10.10.446: Find the length of the curve.y 2t 0 t 2 3 x
 10.10.447: Find the length of the curve. x 2 3t y cosh 3t 0 t 1y
 10.10.448: Find the length of the curve. r 12
 10.10.449: Find the length of the curve. r sin , 0 3
 10.10.450: Find the area of the surface obtained by rotating the given 3, 2cur...
 10.10.451: Find the area of the surface obtained by rotating the given 3, 2cur...
 10.10.452: The curves defined by the parametric equations are called strophoid...
 10.10.453: The curves defined by the parametric equations are called strophoid...
 10.10.454: A family of curves has polar equations where is a positive number. ...
 10.10.455: Find the foci and vertices and sketch the graph.2 9 y 2 8 1
 10.10.456: Find the foci and vertices and sketch the graph.4x 2 y 2 16 x
 10.10.457: Find the foci and vertices and sketch the graph.6y 2 x 36y 55 0 4x
 10.10.458: Find the foci and vertices and sketch the graph.25x 2 4y 2 50x 16y ...
 10.10.459: Find an equation of the ellipse with foci and vertices
 10.10.460: Find an equation of the parabola with focus and directrix .
 10.10.461: Find an equation of the parabola with focus and directrix .
 10.10.462: Find an equation of the ellipse with foci and major axis with lengt...
 10.10.463: Find an equation for the ellipse that shares a vertex and a focus w...
 10.10.464: Show that if is any real number, then there are exactly two lines o...
 10.10.465: Find a pplar equation for the ellipse with focus at the origin,ecce...
 10.10.466: Show that the angles between the polar axis and the asymptotes of t...
 10.10.467: In the figure the circle of radius is stationary, and for every , t...
 10.10.468: A curve is defined by the parametric equations Find the length of t...
 10.10.469: (a) Find the highest and lowest points on the curve . (b) Sketch th...
 10.10.470: What is the smallest viewing rectangle that contains every member o...
 10.10.471: Four bugs are placed at the four corners of a square with side leng...
 10.10.472: A curve called the folium of Descartes is defined by the parametric...
 10.10.473: A circle of radius has its center at the origin. A circle of radius...
Solutions for Chapter 10: PARAMETRIC EQUATIONS AND POLAR COORDINATES
Full solutions for Calculus: Early Transcendentals  6th Edition
ISBN: 9780495011668
Solutions for Chapter 10: PARAMETRIC EQUATIONS AND POLAR COORDINATES
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780495011668. Since 473 problems in chapter 10: PARAMETRIC EQUATIONS AND POLAR COORDINATES have been answered, more than 35344 students have viewed full stepbystep solutions from this chapter. Chapter 10: PARAMETRIC EQUATIONS AND POLAR COORDINATES includes 473 full stepbystep solutions.

Control
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable

Divisor of a polynomial
See Division algorithm for polynomials.

Domain of validity of an identity
The set of values of the variable for which both sides of the identity are defined

Fivenumber summary
The minimum, first quartile, median, third quartile, and maximum of a data set.

Frequency distribution
See Frequency table.

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Measure of an angle
The number of degrees or radians in an angle

Natural numbers
The numbers 1, 2, 3, . . . ,.

Negative linear correlation
See Linear correlation.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Polar axis
See Polar coordinate system.

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Quartic function
A degree 4 polynomial function.

Right triangle
A triangle with a 90° angle.

Root of an equation
A solution.

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n  12d4,

Translation
See Horizontal translation, Vertical translation.