Question

The distance between the directrices of a rectangular hyperbola is 10 units, then distance between is foci is

(a) $10 \sqrt{2}$

(b) 5

(c) $5 \sqrt{2}$

(d) 20

Answer 1

Eccentricity of rectangular hyperbola $=\sqrt{2}$

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

From the given condition,

$\begin{array}{l}\frac{2 a}{\sqrt{2}}=10 \\\Rightarrow \quad 2 a=10 \sqrt{2} \\\end{array}$

Distance between foci $=2 \alpha e=10 \sqrt{2} \cdot \sqrt{2}=20$

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