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 Pintersects 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.

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 Pintersects 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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 35E

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