Question

The distance between the directrices of the hyperbola $x=8sec\theta ,y=8tan\theta$,is

• A. $8\sqrt{2}$
• B. $16\sqrt{2}$
• C. $4\sqrt{2}$
• D. $6\sqrt{2}$

Answer 1

The correct option is A

$8\sqrt{2}$

$Wehave,$

$x=8sec\theta ,y=8tan\theta$

$Onsquaringandsubrtracting:$

$x^2-y^2=8se{c}^2\theta -8ta{n}^2\theta$

$\Rightarrow x^2-y^2=8$

$\Rightarrow \frac{x^2}{8}-\frac{y^2}{8}=1$

$\therefore a=b=8$

$\text{Distance between the directrices of the}$

$heperbola=\frac{2a^2}{\sqrt{a^2+b^2}}$

$Distancebetweenthedirectrices$

$=\frac{2\times 64}{\sqrt{64+64}}$

$=\frac{16}{\sqrt{2}}=8\sqrt{2}$