If distance between the directrices be thrice the distance betwee… - Vidyadip

MCQ

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

A
$\frac{1}{2}$
B
$\frac{2}{3}$
✓
$\frac{1}{\sqrt{3}}$
D
$\frac{4}{5}$

✓

Answer

Correct option: C.

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

(C)
According to the condition, $\frac{2 a }{ e }=3(2 ae )$
$\Rightarrow e =\frac{1}{\sqrt{3}}$

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