 11.11.6.1: If (x, y) are the rectangu lar coo rdinates of a po int P and __ (I...
 11.11.3.1: The distance d from Pl = (2, 5) to P2 __ = (4, 2) is d = . (p.157)
 11.11.7.1: The function f(x) = 3 sin e 4x) has amplitude __ and period __ . (p...
 11.11.2.1: The formula for the distance d from PI = (Xl, yd to P2 = (X2,)'2 ) ...
 11.11.5.1: The sum formula for the sine function is sin(A + B) = ____ . (p.630)
 11.11.4.1: The distance d from PI = (3, 4) to P 2 = ( 2, 1) is d = ____. (p....
 11.1: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.2: Transform the equation r = 6 co s 13 fro m po lar coo rdinates to r...
 11.11.3.2: To complete the square of x2  3x, add __ . (pp. 99101)
 11.11.7.2: Let x = f(t) an d y = get), where f and g are two functions whose c...
 11.11.2.2: To complete the square of x 2  4x, add __ . (pp. 99101)
 11.11.5.2: TIle Doubleangle Formula for the sine function is sin(2t9) = ____ ...
 11.11.4.2: To complete the square of x 2 + 5x, add __ . (pp. 99101 )
 11.2: In 120, identify each equation. If it is a parabola, give its vert...
 11.3: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.3: The po lar equation r = 8 is a co nic who se eccen4  2 sin 13 tri ...
 11.11.3.3: Find the intercepts of the equation l = 16  4x2. (pp. 1651 66)
 11.11.7.3: The parametric equations x = 2 sin t, y = 3 cos t define a(n) ___.
 11.11.5.3: If t9 is acute, the Half angle Formula for the sine function is si...
 11.11.2.3: Use the Square Root Method to find the real solutions of (x + 4)2 =...
 11.11.4.3: Find the intercepts of the equation l = 9 + 4x2 . ( pp. 1 651 66)
 11.4: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.4: The eccentricity e of a parabola is __ , of an ellipse it is __ , a...
 11.11.3.4: The point that is symmetric with respect to the yaxis to the point...
 11.11.7.4: If a circle rolls along a horizontal line without slippage, a point...
 11.11.5.4: If t9 is acute, the Halfangle Formula for the cosine function is c...
 11.11.2.4: The point that is symmetric with respect to the xaxis to the point...
 11.11.4.4: True or False The equation l = 9 + x2 is symmetric with respect to ...
 11.5: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.5: True or False If ( I', e) are po lar coo rdinates, the equation 2 ....
 11.11.3.5: To graph y = (x + If  4, shift the graph of y = x2 to the (left/ri...
 11.11.7.5: True or False Parametric equations definin g a curve are unique.
 11.11.5.5: To transform the equation Ax2 + Bxy + cl + Dx + Ey + F = 0, B=ft.O...
 11.11.2.5: To graph y = (x  3 )2 + 1, shift the graph of y = x 2 to the right...
 11.11.4.5: To graph y = (x  5 )3  4, shift the graph of y = x 3 __ . to the ...
 11.6: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.6: True or False The eccentricity of any parabola is 1.
 11.11.3.6: The standard equation of a circle with center at (2, 3) and radius...
 11.11.7.6: True or False Curves defined using parametric equations have an ori...
 11.11.5.6: Identify the con ic: x 2  2i  x  y  IS = 0 ____.
 11.11.2.6: A(n) __ is the collection of all points in the plane such that the ...
 11.11.4.6: Find the vertical asymptotes, if any, and the horizontal or oblique...
 11.11.4.7: A(n) __ is the collection of points in the plane the difference of ...
 11.7: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.7: In 712, identify the conic that each polar equation represents. Al...
 11.11.3.7: A(n) __ is the collection of all points in the plane the sum of who...
 11.11.7.7: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.7: Identify the conic: x2 + 2xy + 3i  2x + 4y + 10 = 0 ____.
 11.11.2.7: The surface formed by rotating a parabola about its axis of symmetr...
 11.11.4.8: For a hyperbola, the foci lie on a line called the ____ ____ .
 11.8: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.8: In 712, identify the conic that each polar equation represents. Al...
 11.11.3.8: For an ellipse, the foci lie on a line called the __ axis.
 11.11.7.8: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.8: True or False The equation ax 2 + 6i  12y = 0 defines an ellipse i...
 11.11.2.8: True or False The vertex of a parabola is a point on the parabola t...
 11.11.4.9: The asymptotes of the hyperbola '4  9' = 1 are __ and ___.
 11.9: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.9: In 712, identify the conic that each polar equation represents. Al...
 11.11.3.9: For the elliPse : + 5 = 1, the vertices are the points ___ and ___ .
 11.11.7.9: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.9: True or False The equation 3x2 + bxy + 12i = 10 defines a parabola ...
 11.11.2.9: True or False If a light is placed at the focus of a parabola, all ...
 11.11.4.10: True or False The foci of a hyperbola lie on a line called the axis...
 11.10: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.10: In 712, identify the conic that each polar equation represents. Al...
 11.11.3.10: True or False The foci, vertices, and center of an ellipse lie on a...
 11.11.7.10: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.10: True or False To eliminate the xyterm from the equation x 2  2xy ...
 11.11.2.10: True or False The graph of a quadratic function is a parabola.
 11.11.4.11: True or False Hyperbolas always have asymptotes.
 11.11: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.11: In 712, identify the conic that each polar equation represents. Al...
 11.11.3.11: True or False If the center of an ellipse is at the origin and the ...
 11.11.7.11: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.11: In 1120, identify each equation without completing the squares. x2...
 11.11.2.11: In 1118, the graph of a parabola is given. Match each graph to its...
 11.11.4.12: True or False A hyperbola will never intersect its transverse axis.
 11.12: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.12: In 712, identify the conic that each polar equation represents. Al...
 11.11.3.12: True or False A circle is a certain type of ellipse.
 11.11.7.12: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.12: In 1120, identify each equation without completing the squares. 2i...
 11.11.2.12: In 1118, the graph of a parabola is given. Match each graph to its...
 11.11.4.13: In 1316, the graph of a hyperbola is given. Match each graph to it...
 11.13: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.13: In 1324, analyze each equation and graph it. '=1 + co s(
 11.11.3.13: In 1316, the graph of an ellipse is given. Match each graph to its...
 11.11.7.13: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.13: In 1120, identify each equation without completing the squares. 6x...
 11.11.2.13: In 1118, the graph of a parabola is given. Match each graph to its...
 11.11.4.14: In 1316, the graph of a hyperbola is given. Match each graph to it...
 11.14: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.14: In 1324, analyze each equation and graph it. r= 1  sin (
 11.11.3.14: In 1316, the graph of an ellipse is given. Match each graph to its...
 11.11.7.14: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.14: In 1120, identify each equation without completing the squares. 2x...
 11.11.2.14: In 1118, the graph of a parabola is given. Match each graph to its...
 11.11.4.15: In 1316, the graph of a hyperbola is given. Match each graph to it...
 11.15: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.15: In 1324, analyze each equation and graph it. I' = . 4 + 3 sm (
 11.11.3.15: In 1316, the graph of an ellipse is given. Match each graph to its...
 11.11.7.15: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.15: In 1120, identify each equation without completing the squares. 3x...
 11.11.2.15: In 1118, the graph of a parabola is given. Match each graph to its...
 11.11.4.16: In 1316, the graph of a hyperbola is given. Match each graph to it...
 11.16: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.16: In 1324, analyze each equation and graph it. I' =5 + 4 co s ()
 11.11.3.16: In 1316, the graph of an ellipse is given. Match each graph to its...
 11.11.7.16: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.16: In 1120, identify each equation without completing the squares. 4x...
 11.11.2.16: In 1118, the graph of a parabola is given. Match each graph to its...
 11.11.4.17: In 1726, find an equation for the hyperbola described. Graph the e...
 11.17: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.17: In 1324, analyze each equation and graph it. I' =3  6 co s (
 11.11.3.17: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.17: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.17: In 1120, identify each equation without completing the squares. 2i...
 11.11.2.17: In 1118, the graph of a parabola is given. Match each graph to its...
 11.11.4.18: In 1726, find an equation for the hyperbola described. Graph the e...
 11.18: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.18: In 1324, analyze each equation and graph it. I' =  4 + 8 sin ()
 11.11.3.18: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.18: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.18: In 1120, identify each equation without completing the squares. i ...
 11.11.2.18: In 1118, the graph of a parabola is given. Match each graph to its...
 11.11.4.19: In 1726, find an equation for the hyperbola described. Graph the e...
 11.19: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.19: In 1324, analyze each equation and graph it. r=2  sin ()
 11.11.3.19: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.19: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.19: In 1120, identify each equation without completing the squares. x2...
 11.11.2.19: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.20: In 1726, find an equation for the hyperbola described. Graph the e...
 11.20: In 120, identify each equation. If it is a parabola, give its vert...
 11.11.6.20: In 1324, analyze each equation and graph it. r= 2 + 4 co s()
 11.11.3.20: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.20: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.20: In 1120, identify each equation without completing the squares. 2X...
 11.11.2.20: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.21: In 1726, find an equation for the hyperbola described. Graph the e...
 11.21: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.21: In 1324, analyze each equation and graph it. 1'(3  2 sin () = 6
 11.11.3.21: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.21: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.21: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.21: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.22: In 1726, find an equation for the hyperbola described. Graph the e...
 11.22: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.22: In 1324, analyze each equation and graph it. 1'(2  co s () = 2
 11.11.3.22: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.22: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.22: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.22: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.23: In 1726, find an equation for the hyperbola described. Graph the e...
 11.23: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.23: In 1324, analyze each equation and graph it. r= 2 sec () 1
 11.11.3.23: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.23: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.23: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.23: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.24: In 1726, find an equation for the hyperbola described. Graph the e...
 11.24: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.24: In 1324, analyze each equation and graph it. 3 e sc () 1'=csc()  1
 11.11.3.24: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.24: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.24: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.24: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.25: In 1726, find an equation for the hyperbola described. Graph the e...
 11.25: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.25: In 2536, convert each polar equation to a rectangular equation. r ...
 11.11.3.25: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.25: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.25: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.25: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.26: In 1726, find an equation for the hyperbola described. Graph the e...
 11.26: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.26: In 2536, convert each polar equation to a rectangular equation. r ...
 11.11.3.26: In 1726, find the vertices and foci of each ellipse. Graph each eq...
 11.11.7.26: In 726, graph the curve whose parametric equations are given and s...
 11.11.5.26: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.26: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.27: In 2 734, find the center, transverse axis, vertices, foci, and as...
 11.27: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.27: In 2536, convert each polar equation to a rectangular equation. r ...
 11.11.3.27: In 2738, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.27: In 2734, find two different parametric equations for each rectangu...
 11.11.5.27: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.27: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.28: In 2 734, find the center, transverse axis, vertices, foci, and as...
 11.28: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.28: In 2536, convert each polar equation to a rectangular equation. r=...
 11.11.3.28: In 2738, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.28: In 2734, find two different parametric equations for each rectangu...
 11.11.5.28: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.28: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.29: In 2 734, find the center, transverse axis, vertices, foci, and as...
 11.29: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.29: In 2536, convert each polar equation to a rectangular equation. r=...
 11.11.3.29: In 2738, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.29: In 2734, find two different parametric equations for each rectangu...
 11.11.5.29: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.29: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.30: In 2 734, find the center, transverse axis, vertices, foci, and as...
 11.30: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.30: In 2536, convert each polar equation to a rectangular equation. r ...
 11.11.3.30: In 2738, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.30: In 2734, find two different parametric equations for each rectangu...
 11.11.5.30: In 2130, determine the appropriate rotation formulas to use so tha...
 11.11.2.30: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.31: In 2 734, find the center, transverse axis, vertices, foci, and as...
 11.31: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.31: In 2536, convert each polar equation to a rectangular equation. r ...
 11.11.3.31: In 2738, find an equation for each ellipse. Graph the equation. Fo...
 11.11.7.31: In 2734, find two different parametric equations for each rectangu...
 11.11.5.31: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.31: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.32: In 2 734, find the center, transverse axis, vertices, foci, and as...
 11.32: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.32: In 2536, convert each polar equation to a rectangular equation. r=...
 11.11.3.32: In 2738, find an equation for each ellipse. Graph the equation. Fo...
 11.11.7.32: In 2734, find two different parametric equations for each rectangu...
 11.11.5.32: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.32: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.33: In 2 734, find the center, transverse axis, vertices, foci, and as...
 11.33: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.33: In 2536, convert each polar equation to a rectangular equation. r(...
 11.11.3.33: In 2738, find an equation for each ellipse. Graph the equation. Fo...
 11.11.7.33: In 2734, find two different parametric equations for each rectangu...
 11.11.5.33: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.33: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.34: In 2 734, find the center, transverse axis, vertices, foci, and as...
 11.34: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.34: In 2536, convert each polar equation to a rectangular equation. 1'...
 11.11.3.34: In 2738, find an equation for each ellipse. Graph the equation. Fo...
 11.11.7.34: In 2734, find two different parametric equations for each rectangu...
 11.11.5.34: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.34: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.35: In 3538, write an equation for each hyperbola. y=x"Y3 Y=X
 11.35: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.35: In 2536, convert each polar equation to a rectangular equation. r ...
 11.11.3.35: In 2738, find an equation for each ellipse. Graph the equation. Fo...
 11.11.7.35: In 3538, find parametric equations that define the curve shown. y6...
 11.11.5.35: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.35: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.36: In 3538, write an equation for each hyperbola. 3Y=x;<'3 x"'Y = x
 11.36: In 2136, find an equation of the conic described. Graph the equati...
 11.11.6.36: In 2536, convert each polar equation to a rectangular equation. r=...
 11.11.3.36: In 2738, find an equation for each ellipse. Graph the equation. Ve...
 11.11.7.36: In 3538, find parametric equations that define the curve shown. 2...
 11.11.5.36: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.36: In 1936, find the equation of the paraboLa described. Find the two...
 11.11.4.37: In 3538, write an equation for each hyperbola. Y= 2x"5Y= 2x;<'5 x
 11.37: In 3746, identify each conic without completing the squares and wi...
 11.11.6.37: In 3742, find a polar equation for each conic. For each, a focus i...
 11.11.3.37: In 2738, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.37: In 3538, find parametric equations that define the curve shown. y2 3x
 11.11.5.37: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.37: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.38: In 3538, write an equation for each hyperbola. y5 5 5x
 11.38: In 3746, identify each conic without completing the squares and wi...
 11.11.6.38: In 3742, find a polar equation for each conic. For each, a focus i...
 11.11.3.38: In 2738, find an equation for each ellipse. Graph the equation. Ve...
 11.11.7.38: In 3538, find parametric equations that define the curve shown. y(...
 11.11.5.38: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.38: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.39: In 3946, find an equation for the hyperbola described. Graph the e...
 11.39: In 3746, identify each conic without completing the squares and wi...
 11.11.6.39: In 3742, find a polar equation for each conic. For each, a focus i...
 11.11.3.39: In 3942, write an equation for each ellipse. 333 x
 11.11.7.39: In 3942, find parametric equations for an object that moves along ...
 11.11.5.39: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.39: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.40: In 3946, find an equation for the hyperbola described. Graph the e...
 11.40: In 3746, identify each conic without completing the squares and wi...
 11.11.6.40: In 3742, find a polar equation for each conic. For each, a focus i...
 11.11.3.40: In 3942, write an equation for each ellipse. Y33 x
 11.11.7.40: In 3942, find parametric equations for an object that moves along ...
 11.11.5.40: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.40: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.41: In 3946, find an equation for the hyperbola described. Graph the e...
 11.41: In 3746, identify each conic without completing the squares and wi...
 11.11.6.41: In 3742, find a polar equation for each conic. For each, a focus i...
 11.11.3.41: In 3942, write an equation for each ellipse. 3Y333 x
 11.11.7.41: In 3942, find parametric equations for an object that moves along ...
 11.11.5.41: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.41: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.42: In 3946, find an equation for the hyperbola described. Graph the e...
 11.42: In 3746, identify each conic without completing the squares and wi...
 11.11.6.42: In 3742, find a polar equation for each conic. For each, a focus i...
 11.11.3.42: In 3942, write an equation for each ellipse. 3Y33
 11.11.7.42: In 3942, find parametric equations for an object that moves along ...
 11.11.5.42: In 3142, rotate the axes so that the new equation contains no xyt...
 11.11.2.42: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.43: In 3946, find an equation for the hyperbola described. Graph the e...
 11.43: In 3746, identify each conic without completing the squares and wi...
 11.11.6.43: Derive equat ion (b) in Table 5: ep r = ' 1+ e co s(
 11.11.3.43: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.43: In 43 and 44, the parametric equations of four curves are given. Gr...
 11.11.5.43: In 4352, identify each equation without applying a rotation of axe...
 11.11.2.43: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.44: In 3946, find an equation for the hyperbola described. Graph the e...
 11.44: In 3746, identify each conic without completing the squares and wi...
 11.11.6.44: Derive equat ion (c) in Table 5: ep I' = '' I + e sin (
 11.11.3.44: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.44: In 43 and 44, the parametric equations of four curves are given. Gr...
 11.11.5.44: In 4352, identify each equation without applying a rotation of axe...
 11.11.2.44: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.45: In 3946, find an equation for the hyperbola described. Graph the e...
 11.45: In 3746, identify each conic without completing the squares and wi...
 11.11.6.45: Derive equat ion (d) in Table 5: ep r = ' I  e sin (
 11.11.3.45: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.45: In 4548, use a graphing utility to graph the curve defined by the ...
 11.11.5.45: In 4352, identify each equation without applying a rotation of axe...
 11.11.2.45: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.46: In 3946, find an equation for the hyperbola described. Graph the e...
 11.46: In 3746, identify each conic without completing the squares and wi...
 11.11.6.46: Orbit of Mercury T he plan et Mercury t ravels aro un d t he Sun in...
 11.11.3.46: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.46: In 4548, use a graphing utility to graph the curve defined by the ...
 11.11.5.46: In 4352, identify each equation without applying a rotation of axe...
 11.11.2.46: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.47: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.47: In 4752, rotate the axes so that the new equation contains no xyt...
 11.11.3.47: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.47: In 4548, use a graphing utility to graph the curve defined by the ...
 11.11.5.47: In 4352, identify each equation without applying a rotation of axe...
 11.11.2.47: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.48: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.48: In 4752, rotate the axes so that the new equation contains no xyt...
 11.11.3.48: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.48: In 4548, use a graphing utility to graph the curve defined by the ...
 11.11.5.48: In 4352, identify each equation without applying a rotation of axe...
 11.11.2.48: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.49: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.49: In 4752, rotate the axes so that the new equation contains no xyt...
 11.11.3.49: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.49: Projectile Motion Bob throws a ball straight up with an initial spe...
 11.11.5.49: In 4352, identify each equation without applying a rotation of axe...
 11.11.2.49: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.2.50: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.50: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.50: In 4752, rotate the axes so that the new equation contains no xyt...
 11.11.3.50: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.50: Projectile Motion Alice throws a ball straight up with an in itial ...
 11.11.5.50: In 4352, identify each equation without applying a rotation of axe...
 11.11.2.51: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.51: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.51: In 4752, rotate the axes so that the new equation contains no xyt...
 11.11.3.51: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.51: Catching a Train Bill's train leaves at 8:06 AM an d accelerates at...
 11.11.5.51: In 4352, identify each equation without applying a rotation of axe...
 11.11.5.52: In 4352, identify each equation without applying a rotation of axe...
 11.11.2.52: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.52: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.52: In 4752, rotate the axes so that the new equation contains no xyt...
 11.11.3.52: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.52: Catching a Bus Jodi's bus leaves at 5:30 PM an d accelerates at the...
 11.11.5.53: In 5356, apply the rotation formulas (5) to Ax2 + Bxy + ci + Dx + ...
 11.11.2.53: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.53: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.53: In 5358, identify the conic that each polar equation represents an...
 11.11.3.53: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.53: Projectile Motion Ichiro throws a baseball with an initial speed of...
 11.11.5.54: In 5356, apply the rotation formulas (5) to Ax2 + Bxy + ci + Dx + ...
 11.11.2.54: In 3754, find the vertex, focus, and directrix of each paraboLa. G...
 11.11.4.54: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.54: In 5358, identify the conic that each polar equation represents an...
 11.11.3.54: In 4354, analyze each equation; that is, find the centel; foci, an...
 11.11.7.54: Projectile Motion Barry Bonds hit a baseball with an initial speed ...
 11.11.5.55: In 5356, apply the rotation formulas (5) to Ax2 + Bxy + ci + Dx + ...
 11.11.2.55: In 5562, write an equation for each parabola. (0, 1)2 X 2
 11.11.4.55: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.55: In 5358, identify the conic that each polar equation represents an...
 11.11.3.55: In 5564, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.55: Projectile Motion Suppose that Adam hits a golf ball off a cliff 30...
 11.11.5.56: In 5356, apply the rotation formulas (5) to Ax2 + Bxy + ci + Dx + ...
 11.11.2.56: In 5562, write an equation for each parabola. y 2 X
 11.11.4.56: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.56: In 5358, identify the conic that each polar equation represents an...
 11.11.3.56: In 5564, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.56: Projectile Motion Suppose that Karla hits a golf ball off a cliff 3...
 11.11.5.57: Use rotation formulas (5) to sho w that distance is invariant under...
 11.11.2.57: In 5562, write an equation for each parabola. y22l1 O)tX
 11.11.4.57: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.57: In 5358, identify the conic that each polar equation represents an...
 11.11.3.57: In 5564, find an equation for each ellipse. Graph the equation. Ve...
 11.11.7.57: Uniform Motion A Toyota Paseo (traveling east at 40 mph) and a Pont...
 11.11.5.58: Sho w that the graph of the equation x l/2 + il2 = a l/ 2 is part o...
 11.11.2.58: In 5562, write an equation for each parabola. y222(0, 1)2
 11.11.4.58: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.58: In 5358, identify the conic that each polar equation represents an...
 11.11.3.58: In 5564, find an equation for each ellipse. Graph the equation. Fo...
 11.11.7.58: Uniform Motion A Cessna (heading south at 1 20 mph) and a Boeing 74...
 11.11.5.59: Formulate a strategy for discussing and graphing an equation of the...
 11.11.2.59: In 5562, write an equation for each parabola. 2 2 X2
 11.11.4.59: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.59: In 5962, convert each polar equation to a rectangular equation. I'...
 11.11.3.59: In 5564, find an equation for each ellipse. Graph the equation. Fo...
 11.11.7.59: The Green Monster The left field wall at Fenway Park is 310 feet fr...
 11.11.5.60: How does your strategy change if the equat ion is of the follo wing...
 11.11.2.60: In 5562, write an equation for each parabola. 2 I(1, 1)2
 11.11.4.60: In 4760, find the center, transverse axis, vertices, foci, and asy...
 11.60: In 5962, convert each polar equation to a rectangular equation. r ...
 11.11.3.60: In 5564, find an equation for each ellipse. Graph the equation. Ve...
 11.11.7.60: Projectile Motion The position of a projectile fired with an initia...
 11.11.2.61: In 5562, write an equation for each parabola. 22 x
 11.11.4.61: In 6164, graph each function. Be sure to label any intercepts. [Hi...
 11.61: In 5962, convert each polar equation to a rectangular equation. r ...
 11.11.3.61: In 5564, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.61: Show that the parametric equations for a line passing through the p...
 11.11.2.62: In 5562, write an equation for each parabola. 22x
 11.11.4.62: In 6164, graph each function. Be sure to label any intercepts. [Hi...
 11.62: In 5962, convert each polar equation to a rectangular equation. 1'...
 11.11.3.62: In 5564, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.62: Hypocycloid The hypocycloid is a curve defined by the parametric eq...
 11.11.2.63: Satellite Dish A satellite dish is shaped like a paraboloid of revo...
 11.11.4.63: In 6164, graph each function. Be sure to label any intercepts. [Hi...
 11.63: In 6368, graph the curve whose parametric equations are given and ...
 11.11.3.63: In 5564, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.63: In 62, we graphed the hypocycloid. Now graph the rectangular equati...
 11.11.2.64: Constructing a TV Dish A cable TV receiving dish is in the shape of...
 11.11.4.64: In 6164, graph each function. Be sure to label any intercepts. [Hi...
 11.64: In 6368, graph the curve whose parametric equations are given and ...
 11.11.3.64: In 5564, find an equation for each ellipse. Graph the equation. Ce...
 11.11.7.64: Look up the curves called hypocycloid and epicycloid. Write a repor...
 11.11.2.65: Constructing a Flashlight The reflector of a flashlight is in the s...
 11.11.4.65: Fireworks Display Suppose that two people standing 2 miles apart bo...
 11.65: In 6368, graph the curve whose parametric equations are given and ...
 11.11.3.65: In 6568, graph each function. Be sure to label all the intercepts....
 11.11.2.66: Constructing a Headlight A sealedbeam headlight is in the shape of...
 11.11.4.66: Lightning Strikes Suppose that two people standing 1 mile apart bot...
 11.66: In 6368, graph the curve whose parametric equations are given and ...
 11.11.3.66: In 6568, graph each function. Be sure to label all the intercepts....
 11.11.2.67: Suspension Bridge The cables of a suspension bridge are in the shap...
 11.11.4.67: Nuclear Power Plant Some nuclear power plants utilize "natural draf...
 11.67: In 6368, graph the curve whose parametric equations are given and ...
 11.11.3.67: In 6568, graph each function. Be sure to label all the intercepts....
 11.11.2.68: Suspension Bridge The cables of a suspension bridge are in the shap...
 11.11.4.68: An Explosion Two recording devices are set 2400 feet apart, with th...
 11.68: In 6368, graph the curve whose parametric equations are given and ...
 11.11.3.68: In 6568, graph each function. Be sure to label all the intercepts....
 11.11.2.69: Searchlight A searchlight is shaped like a paraboloid of revolution...
 11.11.4.69: Rutherford's Experiment In May 1911, Ernest Rutherford published a ...
 11.69: In 69 and 70, find two different parametric equations for each rect...
 11.11.3.69: Semielliptical Arch Bridge An arch in the shape of the upper half o...
 11.11.2.70: Searchlight A searchlight is shaped like a paraboloid of revolution...
 11.11.4.70: Hyperbolic Mirrors Hyperbolas have interesting reflective propertie...
 11.70: In 69 and 70, find two different parametric equations for each rect...
 11.11.3.70: Semielliptical Arch Bridge The arch of a bridge is a semiellipse wi...
 11.11.2.71: Solar Heat A mirror is shaped like a paraboloid of revolution and w...
 11.11.4.71: The eccentricity e of a hyperbola is defined as the number , a wher...
 11.71: In 71 and 72, find parametric equations for an object that moves al...
 11.11.3.71: Whispering Gallery A hall 100 feet in length is to be designed as a...
 11.11.2.72: Reflecting Telescope A reflecting telescope contains a mirror shape...
 11.11.4.72: A hyperbola for which a = b is called an equilateral hyperbola. Fin...
 11.72: In 71 and 72, find parametric equations for an object that moves al...
 11.11.3.72: Whispering Gallery Jim, standing at one focus of a whispering galle...
 11.11.2.73: Parabolic Arch Bridge A bridge is built in the shape of a parabolic...
 11.11.4.73: Two hyperbolas that have the same set of asymptotes are called conj...
 11.73: Find an equation of the hyperbola whose foci are the vertices of th...
 11.11.3.73: Semielliptical Arch Bridge A bridge is built in the shape of a semi...
 11.11.2.74: Parabolic Arch Bridge A bridge is to be built in the shape of a par...
 11.11.4.74: Prove that the hyperbola l x2    = 1 a2 b2 has the two oblique a...
 11.74: Find an equation of the ellipse whose foci are the vertices of the ...
 11.11.3.74: Semi elliptical Arch Bridge A bridge is to be built in the shape of...
 11.11.2.75: Gateway Arch The Gateway Arch in St. Louis is often mistaken to be ...
 11.11.4.75: Show that the graph of an equation of the form Ax2 + C l + F = 0, A...
 11.75: Describe the collection of points in a plane so that the distance f...
 11.11.3.75: Racetrack Design Consult the figure. A racetrack is in the shape of...
 11.11.2.76: Show that an equation of the form AX2 + Ey = 0, A "* 0, E"* 0 is th...
 11.11.4.76: Show that the graph of an equation of the form AX2 + cl + Dx + y + ...
 11.76: Describe the collection of points in a plane so that the distance f...
 11.11.3.76: Semi elliptical Arch Bridge An arch for a bridge over a highway is ...
 11.11.2.77: Show that an equation of the form cl + Dx = 0, c "* 0, D"* 0 is the...
 11.77: SearcWight A searchlight is shaped like a paraboloid of revolution....
 11.11.3.77: Installing a Vent Pipe A homeowner is putting in a fireplace that h...
 11.11.2.78: Show that the graph of an equation of the form Ax2 + Dx + Ey + F = ...
 11.78: Parabolic Arch Bridge A bridge is built in the shape of a parabolic...
 11.11.3.78: Volume of a Football A football is in the shape of a prolate sphero...
 11.11.2.79: Show that the graph of an equation of the form cl + Dx + Ey + F = 0...
 11.79: Semi elliptical Arch Bridge A bridge is built in the shape of a sem...
 11.11.3.79: In 7982, use the fact that the orbit of a planet about the Sun is ...
 11.80: Whispering Gallery The figure shows the specifications for an ellip...
 11.11.3.80: In 7982, use the fact that the orbit of a planet about the Sun is ...
 11.81: Calibrating Instruments In a test of their recording devices, a tea...
 11.11.3.81: In 7982, use the fact that the orbit of a planet about the Sun is ...
 11.82: Uniform Motion Mary's train leaves at 7:15 AM and accelerates at th...
 11.11.3.82: In 7982, use the fact that the orbit of a planet about the Sun is ...
 11.83: Projectile Motion Drew Bledsoe throws a football with an initial sp...
 11.11.3.83: Show that an equation of the form Ax2 + cl + F = 0, A =f. 0, C =f. ...
 11.84: Formulate a strategy for discussing and graphing an equation of the...
 11.11.3.84: Show that the graph of an equation of the form AX2 + cl + Dx + y + ...
 11.11.3.85: The eccentricity e of an ellipse is defined as the number , where ...
Solutions for Chapter 11: Analytic Geometry
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9780132329033
Solutions for Chapter 11: Analytic Geometry
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. Algebra and Trigonometry was written by and is associated to the ISBN: 9780132329033. Since 494 problems in chapter 11: Analytic Geometry have been answered, more than 87260 students have viewed full stepbystep solutions from this chapter. Chapter 11: Analytic Geometry includes 494 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.