690 CHAPTER 10 Analytic Geometry Answer Problems 11–14 using the figure. 11. Multiple Choice If a 0, > the equation of the parabola is of the form (a) y k a x h 4 2 ( ) ( ) − = − (b) y k a x h 4 2 ( ) ( ) − = − − (c) x h a y k 4 2 ( ) ( ) − = − (d) x h a y k 4 2 ( ) ( ) − = − − 12. The coordinates of the vertex are . 13. Multiple Choice If a 4, = then the coordinates of the focus are . (a) 1, 2 ( ) − (b) 3, 2 ( ) − (c) 7, 2 ( ) (d) 3, 6 ( ) 14. True or False If a 4, = then the equation of the directrix is x 3. = x y V 5 (3, 2) D F Skill Building In Problems 15–22, the graph of a parabola is given. Match each graph to its equation. (A) y x4 2 = (B) x y4 2 = (C) y x4 2 = − (D) x y4 2 = − (E) y x 1 4 1 2 ( ) ( ) − = − (F) x y 1 4 1 2 ( ) ( ) + = + (G) y x 1 4 1 2 ( ) ( ) − = − − (H) x y 1 4 1 2 ( ) ( ) + = − + 15. (2, 1) x y 2 2 22 22 16. x y 3 2 22 (1, 1) 21 17. x y 2 2 22 (1, 1) 22 18. (22, 21) x y 2 2 22 22 19. (21, 21) x y 2 2 22 22 20. (1, 2) x y 2 2 22 22 21. (21, 22) x y 2 2 22 22 22. (21, 21) x y 2 1 23 22 In Problems 23–40, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation. 23. Focus at 4, 0 ; ( ) vertex at 0, 0 ( ) 24. Focus at 0, 2 ; ( ) vertex at 0, 0 ( ) 25. Focus at 0, 3 ; ( ) − vertex at 0, 0 ( ) 26. Focus at 4, 0 ; ( ) − vertex at 0, 0 ( ) 27. Focus at 2, 0 ; ( ) − directrix the line x 2 = 28. Focus at 0, 1 ; ( ) − directrix the line y 1 = 29. Directrix the line y 1 2 ; = − vertex at 0, 0 ( ) 30. Directrix the line x 1 2 ; = − vertex at 0, 0 ( ) 31. Vertex at 0, 0 ; ( ) axis of symmetry the y-axis; containing the point 2, 3 ( ) 32. Vertex at 0, 0 ; ( ) axis of symmetry the x-axis; containing the point 2, 3 ( ) 33. Vertex at 2, 3 ; ( ) − focus at 2, 5 ( ) − 34. Vertex at 4, 2 ; ( ) − focus at 6, 2 ( ) − 35. Vertex at 1, 2; ( ) − − focus at 0, 2 ( ) − 36. Vertex at 3, 0 ; ( ) focus at 3, 2 ( ) − 37. Focus at 3, 4 ; ( ) − directrix the line y 2 = 38. Focus at 2, 4 ; ( ) directrix the line x 4 = − 39. Focus at 3, 2; ( ) − − directrix the line x 1 = 40. Focus at 4, 4 ; ( ) − directrix the line y 2 = − In Problems 41–58, find the vertex, focus, and directrix of each parabola. Graph the equation. 41. x y4 2 = 42. y x8 2 = 43. y x 16 2 = − 44. x y4 2 = − 45. y x 2 8 1 2 ( ) ( ) − = + 46. x y 4 16 2 2 ( ) ( ) + = + 47. x y 3 1 2 ( ) ( ) − = − + 48. y x 1 4 2 2 ( ) ( ) + = − − 49. y x 3 8 2 2 ( ) ( ) + = − 50. x y 2 4 3 2 ( ) ( ) − = − 51. y y x 4 4 4 0 2 − + + = 52. x x y 6 4 1 0 2 + − + = 53. x x y 8 4 8 2 + = − 54. y y x 2 8 1 2 − = − 55. y y x 2 0 2 + − = 56. x x y 4 2 2 − = 57. x x y 4 4 2 − = + 58. y y x 12 1 2 + = − + In Problems 59–66, write an equation for each parabola. 59. (0, 1) (1, 2) x y 2 22 22 60. (1, 2) (2, 1) x y 2 2 22 22 61. (2, 1) (1, 0) x y 2 22 22 62. (0, 21) (2, 0) x y 2 2 22 22
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