MathDB

B1

Part of 1942 Putnam

Problems(1)

Putnam 1942 B1

Source: Putnam 1942

3/1/2022
A square of side 2a2a, lying always in the first quadrant of the xyxy-plane, moves so that two consecutive vertices are always on the xx- and yy-axes respectively. Prove that a point within or on the boundary of the square will in general describe a portion of a conic. For what points of the square does this locus degenerate?
Putnamsquareconics