MathDB
Ellipse

Source: Taiwan NMO 2006

March 21, 2006
conicsellipseanalytic geometrygraphing linesslopegeometrygeometric transformation

Problem Statement

Let the major axis of an ellipse be ABAB, let OO be its center, and let FF be one of its foci. PP is a point on the ellipse, and CDCD a chord through OO, such that CDCD is parallel to the tangent of the ellipse at PP. PFPF and CDCD intersect at QQ. Compare the lengths of PQPQ and OAOA.
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