Chapter Test AN83 17. x y 1 9 2 7 1 2 2 ( ) ( ) + − − = y x 12 (21, 2 1 !7 ) (21, 2 2 !7 ) y 2 2 5 2 (x 1 1) !7 3 y 2 2 5 (x 1 1) !7 3 8 V1 5 (24, 2) F1 5 (25, 2) V2 5 (2, 2) F2 5 (3, 2) (21, 2) 18. x y 3 9 1 4 1 2 2 ( ) ( ) − − − = y x 5 5 y 2 1 5 (x 2 3) 2 3 y 2 1 5 2 (x 2 3) 2 3 V1 5 (0, 1) F1 5 (3 2 !13, 1) F2 5 (3 1 !13, 1) V2 5 (6, 1) (3, 3) (3, 1) (3, 21) 19. Parabola 20. Ellipse 21. Parabola 22. Hyperbola 23. Ellipse 24. x y 9 1 2 2 ′ − ′ = Hyperbola Center at the origin Transverse axis the x -axis ′ Vertices at 1, 0 ( ) ± y x 5 5 x9 y9 (21, 0) (1, 0) 25. x y 2 4 1 2 2 ′ + ′ = Ellipse Center at the origin Major axis the y -axis ′ Vertices at 0, 2 ( ) ± y x 2 (0, 2) y9 x9 (0, 22) 26. y x 4 13 13 2′ = − ′ Parabola Vertex at the origin Focus on the x -axis ′ at 13 13 , 0 − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ y x 5 5 x9 y9 27. Parabola; directrix is perpendicular to the polar axis 4 units to the left of the pole; vertex is 2, . π ( ) y x 5 5 3P 2 4, Polar axis Directrix (2, P) P 2 4, 28. Ellipse; directrix is parallel to the polar axis 6 units below the pole; vertices are 6, 2 π ( ) and 2, 3 2 . π ( ) y x 5 5 Polar axis (3, P) (3, 0) P 2 6, Directrix 3P 2 2, 29. Hyperbola; directrix is perpendicular to the polar axis 1 unit to the right of the pole; vertices are 2 3 , 0 ( ) and 2, . π ( ) − y x 1 3 (22, P) 2 3 , 0 Polar axis Directrix 3P 2 2, P 2 2, 30. y x8 16 0 2 − − = 31. x y x 3 8 4 0 2 2 − − + = 32. y x 2 2 (22, 1) (2, 0) x y4 2 + = 33. y x 7 5 (23, 2) (0, 2) (0, 6) (3, 2) (0, 22) x y 9 2 16 1 2 2 ( ) + − = 34. y x 2 (1, 0) (2, 1) 2 y x 1 + = 35. x t t y t t t x t t y t t t , 2 4, 4 2 , , ( ) ( ) ( ) ( ) = = − + −∞< <∞ = − − = −∞< <∞ 36. π π ( ) ( ) ( ) ( ) = = ≤ ≤ x t t y t t t 4 cos 2 , 3sin 2 , 0 4 37. x y 5 4 1 2 2 − = 38. The ellipse x y 16 7 1 2 2 + = 39. 1 4 ft or 3 in. 40. 19.72 ft, 18.86 ft, 14.91 ft 41. 450 ft 42. (a) Train: x t t y 3 2 , 1 1 2 1 ( ) = = Mary: ( ) ( ) = − = x t t y 6 2 , 3 2 2 (b) Mary won’t catch the train. (c) 5 Mary Train 0 100 t 5 8 43. (a) x t t y t t t 80 cos35 16 80 sin35 6 2 ( ) ( ) ( ) ( ) = ° = − + ° + (b) 2.9932 sec (c) 1.4339 sec; 38.9 ft (d) 196.15 ft (e) 50 0 250 250 Chapter Test (page 752) 1. Hyperbola; center: 1, 0 ; ( ) − vertices: 3, 0 ( ) − and 1,0 ; ( ) foci: 1 13, 0 ( ) − − and 1 13, 0 ; ( ) − + asymptotes: y x 3 2 1 ( ) = − + and y x 3 2 1 ( ) = + 2. Parabola; vertex: 1, 1 2 ; ( ) − focus: 1, 3 2 ; ( ) directrix: y 5 2 = − 3. Ellipse; center: 1, 1 ; ( ) − foci: 1 3, 1 ( ) − − and 1 3, 1 ; ( ) − + vertices: 4, 1 ( ) − and 2, 1 ( )
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