Problem #18

This month's problem is from the 1999 Missouri MAA Collegiate Mathematics Competition.

Let P be a point on the parabola y = x2 other than the origin, (0,0). The normal line to the parabola at P will intersect the parabola at another point, say Q. Find the coordinates of P so that the arclength along the parabola between P and Q is a minimum.

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