Let the eccentricity of an ellipse 
is reciprocal to that of the hyperbola 2x 2 - 2y 2 = 1. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is_____.
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Given,
The eccentricity of an ellipse 
is reciprocal to that of the hyperbola 2x 2 - 2y 2 = 1,
Now eccentricity of rectangular hyperbola 2x 2 - 2y 2 = 1 is e H = 
So 
Now, focus of hyperbola =(±1, 0)
Now given that both curve intersect orthogonally, so ellipse and hyperbola are confocal
So, tor ellipse ae e = 1 
Now length of latusrectum L. R. = 
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