Problem #2

This month's problem is from the 1996 Missouri MAA Collegiate Competition.

Let P be a point in the first quadrant lying on the parabola y = x^2 [other than the origin]. The normal line (the line perpendicular to the tangent line) to the parabola at P will intersect the parabola a another point, say Q. Find the coordinates of P so that the area bounded by the normal line and the parabola is a minimum.

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