Section 10.4 AN77 71. x y 100 36 1 2 2 + = 73. 43.3 ft 75. 24.65 ft, 21.65 ft, 13.82 ft 77. 30 ft 79. The elliptical hole will have a major axis of length 2 41 in. and a minor axis of length 8 in. 81. 91.5 million mi; x y 93 8646.75 1 2 2 2 ( ) + = 83. Perihelion: 460.6 million mi; mean distance: 483.8 million mi; x y 483.8 233,524.2 1 2 2 2 ( ) + = 85. 35 million mi 87. 8 14 cm 29.93 cm ≈ 89. 5 5 4 − 91. (a) Ax Cy F 0 2 2 + + = Ax Cy F 2 2 + = − If A and C are of the same sign and F is of opposite sign, then the equation takes the form x F A y F C 1, 2 2 ( ) ( ) − + − = where F A − and F C − are positive. This is the equation of an ellipse with center at 0, 0 . ( ) (b) If A C, = the equation may be written as x y F A . 2 2 + = − This is the equation of a circle with center at 0, 0 ( ) and radius equal to F A − . 94. Zeros: 5 2 3, 5 2 3; − + x-intercepts: 5 2 3, 5 2 3 − + 95. Domain: x x 5 ; { } ≠ Horizontal asymptote: y 2; = Vertical asymptote: x 5 = 96. 617.1 ft-lb 97. b c B 10.94, 17.77, 38 ≈ ≈ = ° 98. 30 , 7 30 , 13 30 π π π { } 99. 10 7 100. 0.5397 { } − 101. x4 7 − 102. 164 { } 103. 3 25, 3 25 { } − − − + 10.4 Assess Your Understanding (page 716) 7. hyperbola 8. transverse axis 9. b 10. 2,4; 2, 2 ( ) ( ) − 11. 2,6; 2, 4 ( ) ( ) − 12. (a) 1, 1 ( ) − (b) 4 (c) As a changes, the distance between the vertices changes. The value of a represents the distance from the center to the vertices. (d) 4 (e) x y 9 7 1 2 2 − = (f) 5 (g) y x 9 16 1 2 2 − = (h) x2 13. (a) x 2 = (b) c 1 = (c) y k a x h b 1 2 2 2 2 ( ) ( ) − − − = (d) x h a y k b 1 2 2 2 ( ) ( ) − − − = 14. c 15. 2; 3; x 16. y x y x 4 9 ; 4 9 = − = 17. B 19. A 21. x y 8 1 2 2 − = y 5 x 5 V1 5 (21, 0) V2 5 (1, 0) F1 5 (23, 0) F2 5 (3, 0) (0, 22!2) (0, 2!2) y 5 22!2x y 5 2 !2x 23. y x 16 20 1 2 2 − = y 10 x 10 V2 5 (0, 4) F2 5 (0, 6) V1 5 (0, 24) F1 5 (0, 26) y 5 2 x 2 5 5 ! y 5 x 2 5 5 ! (2 , 0) !5 (22 , 0) !5 25. x y 9 16 1 2 2 − = y 10 x 10 V2 5 (3, 0) F2 5 (5, 0) V1 5 (23, 0) F1 5 (25, 0) y 5 2 x 4 3 y 5 x 4 3 (0, 4) (0, 24) 27. y x 36 9 1 2 2 − = y 10 x 10 V2 5 (0, 6) V1 5 (0, 26) y 5 2x y 5 22x (3, 0) (23, 0) F2 5 (0, 3 ) !5 F1 5 (0, 23 ) !5 29. x y 8 8 1 2 2 − = y 5 x 5 F1 5 (24, 0) F2 5 (4, 0) y 5 x y 5 2x (0, 22 ) !2 (0, 2 ) !2 V1 5 (22 , 0) !2 V2 5 (2 , 0) !2 31. x y 25 9 1 2 2 − = Center: 0, 0 ( ) Transverse axis: x-axis Vertices: 5, 0 , 5, 0 ( ) ( ) − Foci: 34, 0 , 34, 0 ( ) ( ) − Asymptotes: y x 3 5 = ± y 10 x 10 V1 5 (25, 0) (0, 23) (0, 3) V2 5 (5, 0) F1 5 (2 , 0) !34 F2 5 ( , 0) !34 y 5 2 x 3 5 y 5 x 3 5 33. x y 4 16 1 2 2 − = Center: 0, 0 ( ) Transverse axis: x-axis Vertices: 2, 0 , 2, 0 ( ) ( ) − Foci: 2 5,0, 2 5,0 ( ) ( ) − Asymptotes: y x2 = ± y 5 x 5 V2 5 (2, 0) V1 5 (22, 0) y 5 22x y 5 2x (0, 4) (0, 24) F2 5 (2 , 0) !5 F1 5 (22 , 0) !5 35. y x 9 1 2 2 − = Center: 0, 0 ( ) Transverse axis: y-axis Vertices: 0, 3 , 0, 3 ( ) ( ) − Foci: 0, 10, 0, 10 ( ) ( ) − Asymptotes: y x3 = ± y 5 x 5 y 5 23x y 5 3x F1 5 (0, 2 ) !10 F2 5 (0, ) !10 V1 5 (0, 23) V2 5 (0, 3) (1, 0) (21, 0) 37. y x 25 25 1 2 2 − = Center: 0, 0 ( ) Transverse axis: y-axis Vertices: 0, 5 , 0, 5 ( ) ( ) − Foci: 0, 5 2 , 0,5 2 ( ) ( ) − Asymptotes: y x = ± y 10 x 10 y 5 2x y 5 x F1 5 (0, 25 ) !2 F2 5 (0, 5 ) !2 V1 5 (0, 25) V2 5 (0, 5) (5, 0) (25, 0) 39. x y 1 2 2 − = 41. y x 36 9 1 2 2 − =
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