Putnam Ellipse Areas Problem

This is a nifty problem from Presh Talwakar.

“This is adapted from the 1994 Putnam, A2. Thanks to Nirman for the suggestion!

Let R be the region in the first quadrant bounded by the x-axis, the line y = x/2, and the ellipse x2/9 + y2 = 1. Let R‘ be the region in the first quadrant bounded by the y-axis, the line y = mx and the ellipse. Find the value of m such that R and R‘ have the same area.”

Answer.

See the Putnam Ellipse Areas Problem for solution.