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

\frac{9}{\sqrt{2}}

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\frac{5}{\sqrt{3}}

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\frac{3}{\sqrt{2}}

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3 \sqrt{2}

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5 \sqrt{3}

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Solution

The correct option is E $3 \sqrt{2}$
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 $= \frac{2 \times 3}{\sqrt{2}} = 3 \sqrt{2}$

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