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Let P be a point on the circle S with both coordinates beings positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve

(x + y) 2 = 3xy
x 2/3 + y 2/3 = 2 4/3
x 2 + y 2 = 2xy
x 2 + y 2 = x 2 y 2

Correct answer: x 2 + y 2 = x 2 y 2

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