Question

The distance between the directrices of the hyperbola $x^2-y^2=9$ is ___ .

• A. $\frac{9}{\sqrt{2}}$
• B. $\frac{3}{\sqrt{2}}$
• C. $6\sqrt{2}$
• D. $3\sqrt{2}$

Answer 1

The correct option is D

$3\sqrt{2}$

The given hyperbola is $x^2-y^2=9$
$\Rightarrow \frac{x^2}{9}-\frac{y^2}{9}=1$
$a=3,b=3,c=\sqrt{a^2+b^2}=3\sqrt{2}$
The equation of the directrices are $x=\pm \frac{a^2}{c}$
Distance between directrices,
$d=\frac{2a^2}{c}=\frac{18}{3\sqrt{2}}=3\sqrt{2}$