1036 CHAPTER 10 Analytic Geometry Graph each equation. Give the domain and range. Identify any that are functions. 43. x 3 = -B1 - y2 16 44. x = -B1 - y2 36 45. y = -21 + x2 46. y = -B1 - x2 25 Write an equation for each conic section with center at the origin. 47. ellipse; vertex at 10, -42, focus at 10, -22 48. ellipse; x-intercept 16, 02, focus at 12, 02 49. hyperbola; focus at 10, 52, transverse axis with length 8 50. hyperbola; y-intercept 10, -22, passing through the point 12, 32 Write an equation for each conic section satisfying the given conditions. 51. parabola with focus at 13, 22 and directrix x = -3 52. parabola with vertex at 1-3, 22 and y-intercepts 10, 52 and 10, -12 53. ellipse with foci at 1-2, 02 and 12, 02 and major axis with length 10 54. ellipse with foci at 10, 32 and 10, -32 and vertex at 10, -72 55. hyperbola with x-intercepts 1-3, 02 and 13, 02 and foci at 1-5, 02 and 15, 02 56. hyperbola with foci at 10, 122 and 10, -122 and asymptotes y = {x Solve each problem. 57. Write the equation of an ellipse consisting of all points in the plane the sum of whose distances from 10, 02 and 14, 02 is 8. 58. Write the equation of a hyperbola consisting of all points in the plane for which the absolute value of the difference of the distances from 10, 02 and 10, 42 is 2. 59. Write the equation of a hyperbola consisting of all points in the plane for which the absolute value of the difference of the distances from 1-5, 02 and 15, 02 is 8. 60. Calculator graphs are shown in choices A–D. Arrange the graphs so that their eccentricities are in increasing order. A. −7.05 −4.65 4.65 7.05 B. −4.7 −3.1 3.1 4.7 C. −9.4 −6.2 6.2 9.4 D. −9.4 −6.2 6.2 9.4
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