A parabola is drawn whose focus is one of the foci of the ellipse `x^2/a^2 + y^2/b^2 = 1` (where a>b) and whose directrix passes through the other focus and perpendicular to the major axes of the ellipse. Then the eccentricity of the ellipse for which the length of latus-rectum of the ellipse and the parabola are same is

Explanation

`x^2/a^2+y^2/b^2=1`

focus of parabola=(ae,0)

Directrix=X-ae

X=-A

`y^2=4AX`

A=ae

Lactus rectum of parabola=Lactus rectum of ellipse

`4A=(2b)^2/a`

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