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Let a, b and lambda positive real numbe...

Let a, b and `lambda` positive real numbers. Suppoose P is an end point of the latus rectum of the parabola `y^(2)=4 lambdax` and suppoose the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` passes thorugh the point. P. if the tangents to the parabola and the ellipse at the point P are perpendicular to each other, then the eccentricity of the ellipse is

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