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General

Easy

Question

If there are exactly two points on the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ whose distance from its centre is same and is equal to $square root of fraction numerator a to the power of 2 end exponent plus 2 b to the power of 2 end exponent over denominator 2 end fraction end root$ then eccentricity of the ellipse is

   $\frac{1}{2}$
$\frac{1}{\sqrt{2}}$
$\frac{1}{\sqrt{3}}$
$\frac{1}{2 \sqrt{2}}$

The correct answer is:
$fraction numerator 1 over denominator square root of 3 end fraction$

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