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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![Problem
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
1/√2.
(b) Show that the line segment PQ has the shortest possible length
when a = 1/√2.
P](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb847239-8296-44e6-a8c0-5fab45b7b532%2F763c1a6c-9a3e-43cd-acf0-ce93c9428e87%2Fj72bsp4_processed.png&w=3840&q=75)
Transcribed Image Text:Problem
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
1/√2.
(b) Show that the line segment PQ has the shortest possible length
when a = 1/√2.
P
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