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Putnam 1994 A2

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July 12, 2014
Putnamgeometryconicsellipsecollege contests

Problem Statement

Let AA be the area of the region in the first quadrant bounded by the line y=x2y = \frac{x}{2}, the x-axis, and the ellipse x29+y2=1\frac{x^2}{9} + y^2 = 1. Find the positive number mm such that AA is equal to the area of the region in the first quadrant bounded by the line y=mx,y = mx, the y-axis, and the ellipse x29+y2=1.\frac{x^2}{9} + y^2 = 1.
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