An ellipse x ² a ² + y ² ~b ² =1, a b and the parabola x ²=4( y + b ) are such that the two foci of the ellipse and the end points of the latus rectum of parabola are the vertices of a square. The eccentricity of the ellipse is

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An ellipse x ² a ² + y ² ~b ² =1, a > b and the parabola x ²=4( y + b ) are such that the two foci of the ellipse and the end points of the latus rectum of parabola are the vertices of a square. The eccentricity of the ellipse is

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Correct answer: B. 2 13

As it is square array l ae =2 4= ( ae -2)²+(1- b )² ~b =-3 ~b =5 a ²=13 a ²=29 ( from realation b ²= a ² (1- e ² ) . ae =2 e = 2 13 array

An ellipse x ² a ² + y ² ~b ² =1, a > b and the parabola x ²=4( y + b ) are such that the two foci of the ellipse and the end points of the latus rectum of parabola are the vertices of a square. The eccentricity of the ellipse is

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