Question

The distance between the directrices of the hyperbola x = 8 sec q, y = 8 tan q is-

• A. 16$\sqrt{2}$
• B. $\sqrt{2}$
• C. 8$\sqrt{2}$
• D. 4$\sqrt{2}$

Answer 1

Answer: (C)

8$\sqrt{2}$

Answer 2

Q x = 8 sec q ; y = 8 tan q

\ Eqn. of hyperbola is Ž $\frac{x^{2}}{8^{2}}$–$\frac{y^{2}}{8^{2}}$= 1; Here a = b = 8

\ e = $\sqrt{1 + \frac{b^{2}}{a^{2}}}$= $\sqrt{1 + \frac{8^{2}}{8^{2}}}$= $\sqrt{2}$

Hence, distance between directrices

=$\frac{2a}{e}$= $\frac{2 \times 8}{\sqrt{2}}$=$8\sqrt{2}$