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.