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If the area of the auxilliary circle of ...

If the area of the auxilliary circle of the ellipse `(x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 (a gt b)` is twice the area of the ellipse, then the eccentricity of the ellipse is

A

`(1)/(sqrt3)`

B

`(1)/(2)`

C

`(1)/(sqrt2)`

D

`(sqrt3)/(2)`

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The correct Answer is:
D
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