Given two perpendicular diameters AB and CD of an ellipse, we say that the diameter A′B′ is conjugate to AB if A′B′ is parallel to the tangent to the ellipse at A. Let A′B′ be conjugate to AB and C′D′ be conjugate to CD.
Prove that the rectangular hyperbola through A′,B′,C′ and D′ passes through the foci of the ellipse. Putnamconicsellipsehyperbola