Locus of Intersection of Tangents at the End of Conjugate Diameters

We create a tangent, then a line HL through the center of the ellipse parallel to the tangent. We then intersect the original tangent with the tangent at this new point L. The locus is seen to be an ellipse. Show that the new ellipse is a dilation of the old ellipse by a factor of sqrt(2). Expressions |
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