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* =
*x*^{2} 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).