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Exercises 21.6, page 597

1. $V (0, - 4), V (0, 4),$ $V (0, - 4), V (0, 4),$
conj. axis $(- 2, 0),$ $(- 2, 0),$ (2,0)
$F (0, - 2 \sqrt{5}), F (0, 2 \sqrt{5})$ $F (0, - 2 \sqrt{5}), F (0, 2 \sqrt{5})$
3. $\begin{array}{l} V (5, 0), V (- 5, 0), \\ F (13, 0), F (- 13, 0) \end{array}$ $\begin{array}{l} V (5, 0), V (- 5, 0), \\ F (13, 0), F (- 13, 0) \end{array}$
5. $\begin{array}{l} V (0, 3), V (0, - 3), F (0, \sqrt{10}), \\ F (0, - \sqrt{10}) \end{array}$ $\begin{array}{l} V (0, 3), V (0, - 3), F (0, \sqrt{10}), \\ F (0, - \sqrt{10}) \end{array}$
7. $\begin{array}{l} V (- \frac{5}{2}, 0), V (\frac{5}{2}, 0), \\ F (- \frac{1}{2} \sqrt{41}, 0), \\ F (\frac{1}{2} \sqrt{41}, 0) \end{array}$ $\begin{array}{l} V (- \frac{5}{2}, 0), V (\frac{5}{2}, 0), \\ F (- \frac{1}{2} \sqrt{41}, 0), \\ F (\frac{1}{2} \sqrt{41}, 0) \end{array}$
9. $\begin{array}{l} V (\frac{2}{3}, 0), V (- \frac{2}{3}, 0), F (\frac{2}{3} \sqrt{10}, 0) \\ F (- \frac{2}{3} \sqrt{10}, 0) \end{array}$ $\begin{array}{l} V (\frac{2}{3}, 0), V (- \frac{2}{3}, 0), F (\frac{2}{3} \sqrt{10}, 0) \\ F (- \frac{2}{3} \sqrt{10}, 0) \end{array}$
11. $\begin{array}{l} V (0, \sqrt{10}), V (0, - \sqrt{10}), \\ F (0, \sqrt{14}), F (0, - \sqrt{14}) \end{array}$ $\begin{array}{l} V (0, \sqrt{10}), V (0, - \sqrt{10}), \\ F (0, \sqrt{14}), F (0, - \sqrt{14}) \end{array}$
13. $\begin{array}{l} V (0, 2), V (0, - 2) \\ F (0, \sqrt{5}), F (0, - \sqrt{5}) \end{array}$ $\begin{array}{l} V (0, 2), V (0, - 2) \\ F (0, \sqrt{5}), F (0, - \sqrt{5}) \end{array}$
15. $\begin{array}{l} V (0.4, 0), V (- 0.4, 0) \\ F (0.9, 0), F (- 0.9, 0) \end{array}$ $\begin{array}{l} V (0.4, 0), V (- 0.4, 0) \\ F (0.9, 0), F (- 0.9, 0) \end{array}$
17. $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1,$ $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1,$ or $16 x^{2} - 9 y^{2} = 144$ $16 x^{2} - 9 y^{2} = 144$
19. $\frac{y^{2}}{100} - \frac{x^{2}}{576} = 1,$ $\frac{y^{2}}{100} - \frac{x^{2}}{576} = 1,$ or $144 y^{2} - 25 x^{2} = 14,400$ $144 y^{2} - 25 x^{2} = 14,400$
21. $\frac{x^{2}}{1} - \frac{y^{2}}{3} = 1,$ $\frac{x^{2}}{1} - \frac{y^{2}}{3} = 1,$ or $3 x^{2} - y^{2} = 3$ $3 x^{2} - y^{2} = 3$
23. $\frac{x^{2}}{5} - \frac{y^{2}}{4} = 1,$ $\frac{x^{2}}{5} - \frac{y^{2}}{4} = 1,$ or $4 x^{2} - 5 y^{2} = 20$ $4 x^{2} - 5 y^{2} = 20$
25. $x^{2} - \frac{y^{2}}{4} = 1,$ $x^{2} - \frac{y^{2}}{4} = 1,$ or $4 x^{2} - y^{2} = 4$ $4 x^{2} - y^{2} = 4$
27. $\frac{x^{2}}{36} - \frac{y^{2}}{64} = 1,$ $\frac{x^{2}}{36} - \frac{y^{2}}{64} = 1,$ or $16 x^{2} - 9 y^{2} = 576$ $16 x^{2} - 9 y^{2} = 576$
29.
31. $\sec^{2} t - \tan^{2} t = x^{2} - y^{2} = 1$ $\sec^{2} t - \tan^{2} t = x^{2} - y^{2} = 1$
33. $(- 2, - 3), (- 2, 3), (2, - 3), (2, 3)$ $(- 2, - 3), (- 2, 3), (2, - 3), (2, 3)$
35. $9 x^{2} - 16 y^{2} - 108 x + 64 y + 116 = 0$ $9 x^{2} - 16 y^{2} - 108 x + 64 y + 116 = 0$
37.
39.
41. $\frac{y^{2}}{16} - \frac{x^{2}}{9} = 1$ $\frac{y^{2}}{16} - \frac{x^{2}}{9} = 1$
43. $9 x^{2} - 16 y^{2} = 144$ $9 x^{2} - 16 y^{2} = 144$
45.
1. $8 x^{2} - y^{2} = 32,$ $8 x^{2} - y^{2} = 32,$
2. $5 x^{2} - 4 y^{2} = 80$ $5 x^{2} - 4 y^{2} = 80$
47. $3 y^{2} - x^{2} = 27$ $3 y^{2} - x^{2} = 27$
49.
51. $i = 6.00 / R$ $i = 6.00 / R$
53.