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A parabola is drawn whose focus is one o...

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

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