MathDB
Putnam 1976 B4

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April 20, 2022
conicsellipsecollege contests

Problem Statement

For a point PP on an ellipse, let dd be the distance from the center of the ellipse to the line tangent to the ellipse at P.P. Prove that (PF1)(PF2)d2(PF_1)(PF_2)d^2 is constant as PP varies on the ellipse, where PF1PF_1 and PF2PF_2 are distances from PP to the foci F1F_1 and F2F_2 of the ellipse.
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