Problem of the Week 1066

Ellipse Deflection

Center an ellipse with major semi-axis 33 and minor semi-axis 5 around the origin in the usual orientation. Let R be the 66×10 rectangle that surrounds it, with sides parallel to the axes.

Let X be the point on the ellipse that minimizes the acute angle between L, the line from the origin through X, and the line tangent to the ellipse at X.

Through which side of the rectangle does line L pass?

Source: Dan Kalman, The maximal deflection of an ellipse, College Math Journal, Sept. 2006.

© Copyright 2006 Stan Wagon. Reproduced with permission.

20 November 2006