1032 CHAPTER 10 Analytic Geometry Solve each problem. 53. If Ax2 + Cy2 + Dx + Ey + F = 0 is the general equation of an ellipse, find the coordinates of its center point by completing the square. 54. Graph the hyperbola x 2 4 - y2 12 = 1 using a graphing calculator. Trace to find the coordinates of several points on the hyperbola. For each of these points P, verify that distance of P from 14, 02 = 23distance of P from the line x = 14. 55. Graph the ellipse x 2 16 + y2 12 = 1 using a graphing calculator. Trace to find the coordinates of several points on the ellipse. For each of these points P, verify that distance of P from 12, 02 = 1 2 3distance of P from the line x = 84. Chapter 10 Test Prep Key Terms 10.1 conic sections parabola focus directrix 10.2 ellipse foci major axis minor axis center vertices conic eccentricity 10.3 hyperbola transverse axis asymptotes fundamental rectangle New Symbols e eccentricity Quick Review Concepts Examples x y V(0, 0) 4 y = –4 F(0, 4) x2 = 16y x y V(0, 0) 4 x = –4 F(4, 0) y2 = 16x 10.1 Parabolas Parabola with Vertical Axis of Symmetry and Vertex 10, 02 The parabola with focus 10, p2 and directrix y = -p has equation x2 =4py. The parabola has vertical axis of symmetry x = 0 and opens up if p 70 or down if p 60. Parabola with Horizontal Axis of Symmetry and Vertex 10, 02 The parabola with focus 1p, 02 and directrix x = -p has equation y2 =4px. The parabola has horizontal axis of symmetry y = 0 and opens to the right if p 70 or to the left if p 60.
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