If P(a, a 2 ) is any point on the parabola y = x 2 , except

Question:

If P(a, a²) is any point on the parabola y = x², except for the origin, let Q be the point where the normal line at P intersects the parabola again (see the figure).
(a) Show that the y-coordinate of Q is smallest when a = 1/√2.
(b) Show that the line segment PQ has the shortest possible length when a = 1√2 .

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