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Putnam 1941 B4

Source: Putnam 1941

February 23, 2022

Putnamconicsellipsehyperbola

Problem Statement

Given two perpendicular diameters

AB

and

CD

of an ellipse, we say that the diameter

A'B'

is conjugate to

AB

if

A'B'

is parallel to the tangent to the ellipse at

A

. Let

A'B'

be conjugate to

AB

and

C'D'

be conjugate to

CD

. Prove that the rectangular hyperbola through

A', B', C'

and

D'

passes through the foci of the ellipse.

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