?If \(P\left(a, a^{2}\right)\) is any first-quadrant point on the parabola \(y=x^{2}\)
Chapter 15, Problem 11(choose chapter or problem)
If \(P\left(a, a^{2}\right)\) is any first-quadrant point on the parabola \(y=x^{2}\), let \(Q\) be the point where the normal line at \(P\) intersects the parabola again (see the figure).
Show that the \(y-coordinate\) of \(Q\) is smallest when \(a=1 / \sqrt{2}\).
how that the line segment \(PQ\) has the shortest possible length when \(a=1 / \sqrt{2}\).
Equation Transcription:
Text Transcription:
P(a,a^2)
y=x^2
Q
P
y-coordinate
a=1/ sqrt 2
PQ
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