Problem of the Week

PROBLEM 234

Consider the ellipse x²+4y²=4. Let R be the region in the first quadrant bounded by the ellipse, the y-axis and the line y=3x. Let R' be the region in the first quadrant bounded by the ellipse, the x-axis and the line y=mx. What does m have to be for R and R' to have the same area?

(For those who like to generalize: Consider the first quadrant of the ellipse centered at the origin with horizontal semiaxis of length a and vertical semiaxis of length b. Given that the area between y=mx and the x-axis is the same as that between y=nx and the y-axis, what is the relationship between m and n?)

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