If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is

\frac{1}{2}

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\frac{2}{3}

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

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\frac{4}{5}

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Solution

The correct option is B $\frac{1}{\sqrt{3}}$
$D i s t a n c e b e t w e e n t h e d i r e c t r i c e s i s \frac{2 a}{e}$

$D i s t a n c e b e t w e e n t h e f o c i i s 2 a e$

$G i v e n : \frac{2 a}{e} = 3 * 2 a e$

$O r, e^{2} = \frac{1}{3}$

$∴ e = \frac{1}{\sqrt{3}}$

Option [C]

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