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Exercises 21.7, page 601

1. Hyperbola, C(3, 2) transverse axis parallel to x-axis; $a = 5, b = 3$ $a = 5, b = 3$
3. Parabola, $(- 1, 2)$ $(- 1, 2)$
5. Hyperbola, (1, 2)
7. Ellipse, $(- 1, 0)$ $(- 1, 0)$
9. Parabola, $(- 3, 1)$ $(- 3, 1)$
11. ${(x + 1)}^{2} = 12 (y - 3)$ ${(x + 1)}^{2} = 12 (y - 3)$ or $x^{2} + 2 x - 12 y + 37 = 0$ $x^{2} + 2 x - 12 y + 37 = 0$
13. $y^{2} = 20 (x - 5)$ $y^{2} = 20 (x - 5)$
15. $\frac{{(x + 2)}^{2}}{25} + \frac{{(y - 2)}^{2}}{16} = 1,$ $\frac{{(x + 2)}^{2}}{25} + \frac{{(y - 2)}^{2}}{16} = 1,$ or $16 x^{2} + 25 y^{2} + 64 x - 100 y - 236 = 0$ $16 x^{2} + 25 y^{2} + 64 x - 100 y - 236 = 0$
17. $\frac{{(y - 1)}^{2}}{16} + \frac{{(x + 2)}^{2}}{4} = 1,$ $\frac{{(y - 1)}^{2}}{16} + \frac{{(x + 2)}^{2}}{4} = 1,$ or $4 x^{2} + y^{2} + 16 x - 2 y + 1 = 0$ $4 x^{2} + y^{2} + 16 x - 2 y + 1 = 0$
19. $\frac{{(y - 2)}^{2}}{1} - \frac{{(x + 1)}^{2}}{3} = 1,$ $\frac{{(y - 2)}^{2}}{1} - \frac{{(x + 1)}^{2}}{3} = 1,$ or $x^{2} - 3 y^{2} + 2 x + 12 y - 8 = 0$ $x^{2} - 3 y^{2} + 2 x + 12 y - 8 = 0$
21. $\frac{{(x + 1)}^{2}}{9} - \frac{{(y - 1)}^{2}}{16} = 1,$ $\frac{{(x + 1)}^{2}}{9} - \frac{{(y - 1)}^{2}}{16} = 1,$ or $16 x^{2} - 9 y^{2} + 32 x + 18 y - 137 = 0$ $16 x^{2} - 9 y^{2} + 32 x + 18 y - 137 = 0$
23. Parabola, $(- 1, - 1)$ $(- 1, - 1)$
25. Parabola, (0, 6)
27. Ellipse, $(- 3, 0)$ $(- 3, 0)$
29. Hyperbola, (0, 4)
31. Hyperbola, $(- 2, 1)$ $(- 2, 1)$
33. Hyperbola, $(- 4, 5)$ $(- 4, 5)$
35. Ellipse, $(1, - 2)$ $(1, - 2)$
37. Hyperbola, (4, 0)
39. Circle, $(\frac{1}{3}, \frac{4}{3})$ $(\frac{1}{3}, \frac{4}{3})$
41. $x^{2} - y^{2} + 4 x - 2 y - 22 = 0$ $x^{2} - y^{2} + 4 x - 2 y - 22 = 0$
43. $y^{2} + 4 x - 4 = 0$ $y^{2} + 4 x - 4 = 0$
45. $y^{2} = 4 p (x - h)$ $y^{2} = 4 p (x - h)$
47. 1 or $- 3$ $- 3$
49. $i^{'} = \sin 2 π t^{'}$ $i^{'} = \sin 2 π t^{'}$
51. ${(x - 95)}^{2} = - \frac{95^{2}}{60} (y - 60)$ ${(x - 95)}^{2} = - \frac{95^{2}}{60} (y - 60)$
53. $\frac{x^{2}}{9.0} + \frac{y^{2}}{16} = 1, \frac{{(x - 7.0)}^{2}}{16} + \frac{y^{2}}{9.0} = 1$ $\frac{x^{2}}{9.0} + \frac{y^{2}}{16} = 1, \frac{{(x - 7.0)}^{2}}{16} + \frac{y^{2}}{9.0} = 1$