A-53 Answers to Selected Exercises 10. parabola –3 x y 0 x = –4y2 – 4y – 3 (–2, – )1 2 vertex: A -2, - 1 2B ; focus: A - 33 16 , - 1 2B ; directrix: x = - 31 16 ; axis: y = - 1 2 10.3 Exercises 1. A 3. D 5. C 7. D 9. x y 2 2 0 – = 1 16 x2 9 y2 1-5, 02, 15, 02; y = { 3 4 x; 1-∞, -44 ´34, ∞2; 1-∞, ∞2 11. x 0 y 8 8 – = 1 25 y2 49 x2 A0, -274 B, A0, 274 B ; y = { 5 7 x; 1-∞, ∞2; 1-∞, -54 ´35, ∞2 13. x 0 y 2 2 x2 – y2 = 9 A -322, 0B , A322, 0B; y = {x; 1-∞, -34 ´33, ∞2; 1-∞, ∞2 15. x 0 y 5 3 9x2 – 25y2 = 225 A -234, 0B , A 234, 0B ; y = { 3 5 x; 1-∞, -54 ´35, ∞2; 1-∞, ∞2 17. y x 0 2 4y2 – 25x2 = 100 5 A0, -229 B , A0, 229 B ; y = { 5 2 x; 1-∞, ∞2; 1-∞, -54 ´35, ∞2 19. x y 9x2 – 4y2 = 1 1 0 1 Q- 213 6 , 0R , Q 213 6 , 0R ; y = { 3 2 x; A -∞, - 1 3D ´C 1 3 , ∞B ; 1-∞, ∞2 21. x y 2 2 (4, 7) (y – 7)2 36 (x – 4)2 64 – = 1 0 14, -32, 14, 172; y = { 3 4 1x - 42 + 7; 1-∞, ∞2; 1-∞, 14 ´313, ∞2 23. x y 10 –10 (–3, 2) (x + 3)2 16 (y – 2)2 9 – = 1 0 1-8, 22, 12, 22; y = { 3 4 1x + 32 + 2; 1-∞, -74 ´31, ∞2; 1-∞, ∞2 25. x y 16(x + 5)2 – (y – 3)2 = 1 1 –1 (–5, 3) 0 A -5 - 217 4 , 3B, A -5 + 217 4 , 3B ; y = {41x + 52 + 3; A -∞, - 21 4 D ´C - 19 4 , ∞B ; 1-∞, ∞2 27. x y 1 1 = 1 + 16 x2 3 y 0 1-∞, ∞2; 33, ∞2; function 29. x y 1 5 1 5 5x = – 1 + 4y2 0 A -∞, - 1 5D ; 1-∞, ∞2 8. parabola x y 1 –1 1 (–1, –3) 8(x + 1) = (y + 3)2 vertex: 1-1, -32; focus: 11, -32; directrix: x = -3; axis: y = -3 9. ellipse x y 0 (–3, –2) = 1 36 (y + 2)2 25 (x + 3)2 + center: 1-3, -22; vertices: 1-3, 42, 1-3, -82; foci: A -3, -2 + 211 B , A -3, -2 - 211 B [10.1, 10.2] 6. parabola –3 –4 x y 0 (–3, –4) y + 4 = (x + 3)2 vertex: 1-3, -42; focus: A -3, - 15 4 B ; directrix: y = - 17 4 ; axis: x = -3 7. ellipse x y 0 2 –2 3 –3 4x2 + 9y2 = 36 center: 10, 02; vertices: 1-3, 02, 13, 02; foci: A -25, 0B , A 25, 0B 31. 1x + 322 2 - 1y + 122 11 = 1; 1-3, -12; horizontal transverse axis 33. 1y - 522 49 - 1x + 422 25 = 1; 1-4, 52; vertical transverse axis 35. 1x - 822 9 - 1y + 222 7 = 1; 18, -22; horizontal
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