AN74 Answers: Chapter 10 13. z e z e z e 2 2 , 2 2 , 2 2 i i i 0 3 2 9 1 3 8 9 2 3 14 9 = = = π π π ⋅ ⋅ ⋅ 2 Imaginary axis Real axis 2 z1 5 2 3 2e 8p/9 i . ! z2 5 2 3 2e ! z0 5 2 3 2e 2p ––– 9 ! 2p/9 i . 14p/9 i . 14. v 52, 52 = 〈 − 〉 15. = v 10 16. = = − u v v 2 2 , 2 2 17. 315° off the positive x-axis 18. v i j 5 2 5 2 = − 19. v v i j 2 v 6 10 1 2 3 + − = − 20. Vectors v1 and v4 are parallel. 21. Vectors v2 and v3 are orthogonal. 22. 172.87° 23. i j k 9 5 3 − − + 24. 57.7 , 143.3 , 74.5 α β γ ≈ ° ≈ ° ≈ ° 25. 115 26. The cable must be able to endure a tension of approximately 670.82 lb. Cumulative Review (page 679) 1. 3, 3 { } − 2. y x 3 3 = 3. x y 1 9 2 2 ( ) + − = y x 5 5 (0, 22) (23, 1) (0, 1) (3, 1) (0, 4) 4. x x 1 2 or , 1 2 { } ( ) < −∞ 5. Symmetry with respect to the y-axis 6. y x 4 2 (1, 0) (e, 1) 1 e , 1 7. y 1.25 x 2P 8. y 1.25 x 2P 9. 6 π − 10. y 4.5 x 4 x 5 3 y 5 4 11. 3P 4 U 5 5P 4 U 5 7P 4 U 5 P 4 U 5 P 3 U 5 y x 1 2 U 5 P r 5 2 U 5 0 12. Amplitude: 4; period: 2 CHAPTER 10 Analytic Geometry 10.2 Assess Your Understanding (page 689) 7. parabola; axis of symmetry 8. latus rectum 9. (a) 6 (b) right (c) 3; 3 (d) 1, 2 ( ) (e) y x 2 12 1 2 ( ) ( ) − = − (f) 3, 2 ( ) − (g) 10 (h) left (i) y x 2 20 3 2 ( ) ( ) − = − + 10. (a) 0,0; 0, 2;2 ( ) ( ) − (b) Down (c) 0,0 ; 0,2 ;2 ( ) ( ) (d) Up (e) x y y 2; 1, 3 ; 1 8 3 ; 1 2 ( ) ( ) ( ) − = − = 11. c 12. 3, 2 ( ) 13. d 14. F 15. B 17. E 19. H 21. C 23. y x 16 2 = y 20 x 20 (4, 8) (4, 28) D: x 5 24 F 5 (4, 0) V 5 (0, 0) 25. x y 12 2 = − y 10 x 10 (6, 23) (26, 23) D: y 5 3 F 5 (0, 23) V 5 (0, 0) 27. y x8 2 = − y 5 x 5 (22, 4) (22, 24) D: x 5 2 F 5 (22, 0) V 5 (0, 0) 29. x y2 2 = 1 2 1, 1 2 0, y 2.5 x 2.5 (2, 2) (22, 2) 1 2 D: y 5 2 F 5 V 5 (0, 0) 1 2 21, 31. x y 4 3 2 = y 4 x 2.5 (2, 3) (22, 3) 2 , 3 1 3 2 2 , 3 1 3 1 3 0, F 5 1 3 D: y 5 2 V 5 (0, 0) 33. x y 2 8 3 2 ( ) ( ) − = − + y 10 x 10 (22, 25) (6, 25) D: y 5 21 F 5 (2, 25) V 5 (2, 23) 35. y x 2 4 1 2 ( ) ( ) + = + y 5 x 5 (0, 24) (0, 0) D: x 5 22 F 5 (0, 22) V 5 (21, 22) 37. x y 3 4 3 2 ( ) ( ) + = − y 8 x 2 (21, 4) (25, 4) D: y 5 2 F 5 (23, 4) V 5 (23, 3) 39. y x 2 8 1 2 ( ) ( ) + = − + y 2 x 2 (23, 2) F 5 (23, 22) V 5 (21, 22) D: x 5 1 (23, 26) 41. Vertex: 0, 0 ; ( ) focus: 0, 1 ; ( ) directrix: y 1 = − y 2.5 x 2.5 (2, 1) (22, 1) V 5 (0, 0) D: y 5 21 F 5 (0, 1) 43. Vertex: 0, 0 ; ( ) focus: 4, 0 ; ( ) − directrix: x 4 = y 10 x 10 (24, 8) (24, 28) D: x 5 4 F 5 (24, 0) V 5 (0, 0) 45. Vertex: 1, 2 ; ( ) − focus: 1, 2 ; ( ) directrix: x 3 = − y 8 x 5 (1, 6) (1, 22) V 5 (21, 2) F 5 (1, 2) D: x 5 23
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