In an ellipse the distance between the foci is one third of the distance between the directrices, then its $e$ is

\frac{1}{2}

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\frac{1}{\sqrt{3}}

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

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\frac{1}{3}

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Solution

The correct option is A $\frac{1}{\sqrt{3}}$
Given,
$2 a e = \frac{1}{3} \frac{2 a}{e}$

$e^{2} = \frac{1}{3}$

$e = \frac{1}{\sqrt{3}}$

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