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There are exactly two points on the elli...

There are exactly two points on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)`=1 whose distance from the centre of the ellipse are equal to `sqrt((3a^2-b^2)/(3))`. Eccentricity of this ellipse is

A

`1/2`

B

`sqrt1/2`

C

`1/sqrt3`

D

`1/sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
A
From the given data, `(3a^(2)-b^(2))/(3)=b^(2)`
`implies 3a^(2)=4b^(2)" "therefore e^(2)=1-b^(2)//a^(2)`
`e=sqrt(1-3//4)=1//2`.
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