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Conics proof question (1 Viewer)

cutemouse

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Hello, could anyone please help me with the following question? Thanks

A and B are the extremities of the major axis of an ellipse. CD is any line parallel to the minor axis. P is any point on the ellipse and the lines PA and PB cut the line CD at H and K respectively. Show that the tangent at P passes through the midpoint of HK.
 

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