SalasSV_09_03_ex_ans

SalasSV_09_03_ex_ans - ANSWERS TO ODD-NUMBERED EXERCISES...

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Unformatted text preview: ANSWERS TO ODD-NUMBERED EXERCISES 25. center (0, 0) transverse axis 2 vertices ( ± 1, 0) √ foci ( ± 2, 0) asymptotes y = ± x y A-67 27. center (0, 0) transverse axis 6 x y 29. center (0, 0) transverse axis 8 x y vertices ( ± 3, 0) foci ( ± 5, 0) asymptotes y = ± 4 x 3 vertices (0, ±4) foci (0, ±5) asymptotes y = ± 4 x 3 x 31. center (1, 3) transverse axis 6 vertices (4, 3) and (−2, 3) foci (6, 3) and (−4, 3) asymptotes y = ± 4 (x − 1) + 3 3 35. d ( F1 , F2 ) + k = 2(c + a) y (1,3) 33. center (1, 3) transverse axis 4 vertices (1, 5) and (1, 1) √ foci (1, 3 ± 5) asymptotes y = 2x + 1, y = −2x + 5 y (1,3) x x √ 37. 2 π 2 a4 − A2 /π a 39. (5 ± 5 21 √ 5, 0) √ √ √ √√ 41. center (0, 0), vertices (1, 1) and (−1, −1), foci ( 2, 2) and (− 2, − 2), asymptotes x = 0 and y = 0, transverse axis 2 2 √ √ 43. [2 3− ln (2 + 3)]ab 45. 3 47. 4 . 49. E1 is fatter than E2 , more like a circle 5 5 51. The ellipse tends to a line segment of length 2a. 53. x2 /9 + y2 = 1 55. 5 3 57. √ 2 59. The branches of H1 open up less quickly than the branches of H2 . 61. The hyperbola tends to a pair of parallel lines separated by the transverse axis. 63. about 0.25 mile west and 1.46 miles north of point A SECTION 9.3 1. −7. See figure to the right. 17. [1, 1 π 2 9. (0, 3) 11. (1, 0) 13. ( − 3 , 2 3 2 √ 3) 15. (0, −3) 2 1, 1 π 3 + 2nπ ], [ − 1, 3 π 2 + 2nπ ] 19. [3, π + 2nπ ], [ − 3, 2nπ ] 23. [8, 1 π + 2nπ ], [ − 8, 7 π + 2nπ ] 6 6 11 π] 6 –1, 1 π 3 polar axis – 1π √ √ 21. [2 2, 7 π + 2nπ ], [ − 2 2, 3 π + 2nπ ] 4 4 25. 2 2 r1 + r2 − 2r1 r2 cos (θ1 − θ2 ) 2 π] 3 27. (a) [ 1 , 2 1 π 3 (b) [ 1 , 5 π ] 26 (c) [ 1 , 7 π ] 26 4, 5 π 4 29. (a) [2, (b) [2, 5 π] 3 (c) [2, 31. symmetry about the x-axis 33. no symmetry about the coordinate axes; no symmetry about the origin 35. symmetry about the origin 43. θ = π/4 37. r cos θ = 2 39. r 2 sin 2θ = 1 41. r = 4 sin θ 45. r = 1 − cos θ 47. r 2 = sin 2θ √ 53. the parabola y2 = 4(x + 1) 51. the line y = 3x 57. the line y = 2x 63. (x − 59. 3x2 + 4y2 − 8x = 16, ellipse 49. the horizontal line y = 4 55. the circle x2 + y2 = 3x b2 a a2 + b2 ) + ( y − )2 = ; center: 2 2 4 61. y2 = 8x + 16, parabola √ ba d a2 + b 2 , 65. r = , radius: 22 2 2 − cos θ SECTION 9.4 1. 3. 4 5. 7. 3 –π 1 4 ...
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