Question

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

• A. $\frac{9}{\sqrt{2}}$
• B. $\frac{5}{\sqrt{3}}$
• C. $\frac{3}{\sqrt{2}}$
• D. $3\sqrt{2}$
• E. $5\sqrt{3}$

Answer 1

Answer: (D)

Distance between the directrices
$=\frac{2 a}{e}$
Now, equation of hyperbola is
$x^{2}-y^{2}=9$
It is a rectangular hyperbola and its eccentricity is always $\sqrt{2}$.
$\therefore $ Required distance
$=\frac{2 \times 3}{\sqrt{2}}=3 \sqrt{2}$