A-52 Answers to Selected Exercises 51. (a) y = 11 5625 x2 (b) 127.8 ft 53. 6 ft 55. (a) 2000 ft (b) y = 1000 - 0.00025x2 (c) no 57. (a) 0 0 1000 1500 Moon Mars y1 = !3x – x 2 1.3 968 y2 = !3x – x 2 6.3 1936 (b) Mars: 230 ft; moon: 558 ft 59. a + b + c = -5; 4a - 2b + c = -14; 4a + 2b + c = -10 60. 51-2, 1, -426 61. It opens to the left because a = -2 and -2 60. 62. x = -2y2 + y - 4 10.2 Exercises 1. (a) A (b) C (c) D (d) B 3. 3-4, 44; 3-3, 34; 10, 02; 1-4, 02, 14, 02; A -27 , 0B , A 27 , 0B 5. 3-3, 74; 3-1, 34; 12, 12; 1-3, 12, 17, 12; A2 - 221 , 1B , A2 + 221 , 1B 7. x y 1 0 1 + = 1 25 x2 9 y2 1-4, 02, 14, 02; 3-5, 54; 3-3, 34 9. x y 1 3 + y2 = 1 9 x2 0 A -222, 0B , A222, 0B; 3-3, 34; 3-1, 14 11. 9x2 + y2 = 81 x y 0 2 2 A0, -622 B , A0, 622 B; 3-3, 34; 3-9, 94 13. x y 1 0 1 4x2 = 100 – 25y2 A -221, 0B , A 221, 0B; 3-5, 54; 3-2, 24 15. x y (2, 1) (x – 2)2 25 ( y – 1)2 4 + = 1 0 A2 - 221, 1B , A2 + 221, 1B; 3-3, 74; 3-1, 34 17. x 8 2 y (–3, 2) 0 (x + 3)2 16 ( y – 2)2 36 + = 1 A -3, 2 - 225 B , A -3, 2 + 225 B; 3-7, 14; 3-4, 84 19. x 2 25 + y2 16 = 1 21. x2 5 + y2 9 = 1 23. 1x - 322 25 + y - 122 16 = 1 25. x2 9 + y2 25 = 1 27. x 2 72 + y2 81 = 1 29. x2 25 + y2 9 = 1 31. 9x2 28 + 9y2 64 = 1 (b) y4 = −y3 −40 −60 40 60 y2 = −y1 y3 = 38.2 Ä 1 − (x − 9.8106)2 39.42 y1 = Ë30.1 2 − (x − 0.2709)2 61. 323 units Chapter 10 Quiz [10.1, 10.2] 1. (a) B (b) A (c) E (d) C (e) D [10.1] 2. 1y - 222 = 121x + 12 3. x2 = -2y [10.2] 4. 1x - 3 2 16 + 1y + 222 25 = 1 5. 1x + 322 9 + 1y - 722 25 = 1 33. x y 0 5 2 –5 = 1 – 25 x2 2 y 3-5, 54; 30, 24; function 35. x y 1 1 8 –8 x = – 1 – 64 y2 0 3-1, 04; 3-8, 84 37. −4.1 −6.6 4.1 6.6 y2 = −2 Ä 1 − x2 16 y1 = 2 Ä 1 − x2 16 39. −8.2 −9.9 8.2 9.9 y1 = 3 Ä 1 − (x − 3)2 25 y2 = −3 Ä 1 − (x − 3)2 25 41. 1x + 122 25 + 1y - 522 4 = 1; 1-1, 52; 1-6, 52, 14, 52; 1-1, 32, 1-1, 72 43. x 2 9 + 1y + 622 49 = 1; 10, -62; 10, -132, 10, 12; 1-3, -62, 13, -62 45. 1x - 722 12 + 1y - 222 = 1; 17, 22; A7 - 223, 2B, A7 + 223, 2B; 17, 12, 17, 32 47. 1x - 922 6 + 1y + 622 8 = 1; 19, -62; A9, -6 - 2 22B, A9, -6 + 222B; A9 - 26, -6B, A9 + 26, -6B 49. 1 2 51. 0.65 53. Fixing a string to two points (foci) and sweeping a curve as shown will sketch an ellipse, because the sum of the distances from the two fixed points to the pencil’s tip remains constant. 55. 12 ft tall 57. 55 million mi 59. (a) Neptune: 1x - 0.270922 30.12 + y2 30.12 = 1; Pluto: 1x - 9.810622 39.42 + y2 38.22 = 1
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