Homothetic_Conics

Homothetic conics

Consider two homothetic ellipses (w.r. to their common center) and from a pont B of the outer one draw a tangent to the inner ellipse cutting again the outer at C. Show that the contact point D is the middle of BC.

If we consider the direction BC and define the involution F, of the conic b, which to every point X on b corresponds Y such that XY is parallel to BC, then the line of fixed points of F coincides with the conjugate diameter of the direction BC, passing through D.

Notice tha C'C is tangent of the inner ellipse only if the homothety ratio is MN/OP = 2.

Get to the topic handling the above involution in the file: Conjugate_Diameter_Involution.html

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