Problem #22

This month's problem is a variant of one from the 1999 Missouri MAA Collegiate Mathematics Competition [see Advanced Problem #18].

Let P be a point on the parabola y = x2 other than the origin, (0,0). The parabola and the normal line to the parabola at P will determine a bounded region. Find the coordinates of P so that the total perimeter of the bounded region is a minimum.

Note: You may give your answer numerically (say to five decimal places).

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