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Question

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

A
12
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B
23
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C
13
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D
45
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Solution

The correct option is C 13
Let the equation of ellipse be
x2a2+y2b2=1(a>b)
Since, it is an standard ellipse
Distance between the directrices =2×ae
And distance between the foci =2×ae.

Given, 2ae=3×2ae
e=13 (a0)

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