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

Question

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

(a) $16 \sqrt{2}$

(b) $\sqrt{2}$

(c) $8 \sqrt{2}$

(d) $4 \sqrt{2}$

Answer 1

Now, $\left(\frac{x}{8}\right)^2-\left(\frac{y}{8}\right)^2=\sec ^2 \theta-\tan ^2 \theta=1$ $\Rightarrow \quad x^2-y^2=64$

Here, it is a rectangular hyperbola, so eccentricity is $\sqrt{2}$

$\therefore$ Distance between directrices $=\frac{2 a}{e}=\frac{2 \times 8}{\sqrt{2}}=8 \sqrt{2}$

So, The correct option of this question will be (C).