Product of perpendiculars from foci of an ellipse to any tangent?

For a given fixed ellipse, with a tangent line to any point on that ellipse, consider the perpendiculars from the two foci to that tangent. What can be said of the product of these two distances?

A messy analytic proof is not difficult, but can anyone find an elegant demonstration of the result?

Indica2013-05-08T01:12:14Z

Favorite Answer

Chapter 2, p56

http://archive.org/stream/cu31924068659097#page/n3/mode/2up

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