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Putnam 1942 A4

Source: Putnam 1942

March 1, 2022
Putnamconics

Problem Statement

Find the orthogonal trajectories of the family of conics (x+2y)2=a(x+y)(x+2y)^{2} = a(x+y). At what angle do the curves of one family cut the curves of the other family at the origin?
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