AN82 Answers: Chapter 10 55. (a) x t t y t t t 40 cos45 4.9 40 sin45 300 2 ( ) ( ) ( ) ( ) = ° = − + ° + (b) 11.23 sec (c) 317.52 m (d) 2.89 sec; 340.82 m (e) 400 2160 0 320 57. (a) Camry: x t t y t 40 5, 0; ( ) ( ) = − = Chevy Impala: x t y t t 0, 30 4 ( ) ( ) = = − (b) d t t 40 5 30 4 2 2 ( ) ( ) = − + − (c) 7 0 0 0.2 (d) 0.2 mi; 7.68 min (e) 4 26 24 6 59. (a) x t v t y t t v t 2 2 , 16 2 2 3 0 2 0 ( ) ( ) = = − + + (b) Maximum height is 139.1 ft. (c) The ball is 272.25 ft from home plate. (d) Yes, the ball will clear the wall by about 99.5 ft. 61. The orientation is from x y , 1 1 ( ) to x y , . 2 2 ( ) 63. x m R m m y m mR m m 1 1 , 2 1 , 2 2 2 ( ) ( ) ( ) = − + = + −∞< <∞ 67. y x 2 4 6 2 4 6 22 22 24 26 24 26 68. y x 2P y 5 2 cos(2x) sin y 5 x 2 3 11. y x8 2 = − y x 5 5 V 5 (0, 0) F 5 (22, 0) (22, 4) (22, 24) D: x 5 2 12. y x 4 12 1 2 2 − = y x 5 5 F1 5 (0, 24) V1 5 (0, 22) V2 5 (0, 2) F2 5 (0, 4) y 5 2 3 !3 x 3 y 5 !3 x (2!3, 0) (22!3, 0) 13. x y 16 7 1 2 2 + = y x 5 5 F1 5 (23, 0) V1 5 (24, 0) F2 5 (3, 0) V2 5 (4, 0) (0, !7) (0, 2!7) Review Exercises (page 750) 1. Parabola; vertex 0, 0 , ( ) focus 4, 0 , ( ) − directrix x 4 = 2. Hyperbola; center 0, 0 , ( ) vertices 5, 0 ( ) and 5, 0 , ( ) − foci 26, 0 ( ) and 26, 0 , ( ) − asymptotes y x 1 5 = and y x 1 5 = − 3. Ellipse; center 0, 0 , ( ) vertices 0, 5 ( ) and 0, 5, ( ) − foci 0, 3 ( ) and 0, 3 ( ) − 4. ( ) = − − x y 4 1 : 2 Parabola; vertex 0, 1 , ( ) focus 0, 0 , ( ) directrix y 2 = 5. − = x y 2 8 1: 2 2 Hyperbola; center 0, 0 , ( ) vertices 2, 0 ( ) and 2, 0 , ( ) − foci 10, 0 ( ) and 10, 0 , ( ) − asymptotes y x2 = and y x2 = − 6. x y 2 2 2 : 2 ( ) ( ) − = + Parabola; vertex 2, 2 , ( ) − focus 2, 3 2 , ( ) − directrix y 5 2 = − 7. y x 2 4 1 1: 2 2 ( ) ( ) − − − = Hyperbola; center 1, 2 , ( ) vertices 1, 4 ( ) and 1,0 , ( ) foci 1, 2 5 ( ) + and 1,2 5 , ( ) − asymptotes y x 2 2 1 ( ) − = ± − 8. ( ) ( ) − + − = x y 2 9 1 4 1: 2 2 Ellipse; center 2, 1 , ( ) vertices 5, 1 ( ) and 1, 1 , ( ) − foci 2 5, 1 ( ) + and 2 5,1 ( ) − 9. x y 2 4 1 : 2 ( ) ( ) − = − + Parabola; vertex 2, 1 , ( ) − focus 2, 2, ( ) − directrix y 0 = 10. x y 1 4 1 9 1: 2 2 ( ) ( ) − + + = Ellipse; center 1, 1 , ( ) − vertices 1, 2 ( ) and 1, 4, ( ) − foci 1, 1 5 ( ) − + and 1, 1 5 ( ) − − 69. Approximately 2733 miles 70. (a) Simple harmonic (b) 2 m (c) 2 sec π (d) 2 oscillations sec π 71. y x2 11 2 = − 72. x 1 3 2 ( ) − + 73. 6 2 4 − 74. 7 3{ } 75. c 2 3 3 = 14. x y 2 4 3 2 ( ) ( ) − = − + y x 2 8 D: y 5 22 F 5 (2, 24) V 5 (2, 23) (0, 24) (4, 24) 15. x y 2 3 3 1 2 2 ( ) ( ) + − + = y x 2 2 V1 5 (23, 23) F1 5 (24, 23) V2 5 (21, 23) F2 5 (0, 23) (22, 23 2 !3 ) (22, 23 1 !3 ) (22, 23) y 1 3 5 2!3 (x 1 2) y 1 3 5 !3 (x 1 2) 16. x y 4 16 5 25 1 2 2 ( ) ( ) + + − = x y 29 10 V2 5 (24, 10) V1 5 (24, 0) F2 5 (24, 8) F1 5 (24, 2) (28, 5) (24, 5) (0, 5)
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