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2. Parabolic tangents and peculiar perpendicularities! a. Let la and lo be tangent lines to the parabola y=x2 at x=a and x-b, respectively, where a#0. 1. For what values of a and b are la and lb perpendicular to one another? 2. Make a sketch to illustrate one case of your answer, for a=2. b. The tangent line to the parabola x2=4y at the point P(a, b) meets the line y=-1 at the point A. Suppose B is the point (0,1). 1. Find the x-coordinate of the point A in terms of a. 2. Show that for all a+0, ABP is a right angle.

2. Parabolic tangents and peculiar perpendicularities! a. Let la and lo be tangent lines to the parabola y=x2 at x=a and x-b, respectively, where a#0. 1. For what values of a and b are la and lb perpendicular to one another? 2. Make a sketch to illustrate one case of your answer, for a=2. b. The tangent line to the parabola x2=4y at the point P(a, b) meets the line y=-1 at the point A. Suppose B is the point (0,1). 1. Find the x-coordinate of the point A in terms of a. 2. Show that for all a+0, ABP is a right angle.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2. Parabolic tangents and peculiar perpendicularities! a. Let la and lb be tangent lines to the parabola y=x² at x=a and x=b, respectively, where a#0. 1. For what values of a and b are la and lb perpendicular to one another? 2. Make a sketch to illustrate one case of your answer, for a=2. b. The tangent line to the parabola x2=4y at the point P(a, b) meets the line y=-1 at the point A. Suppose B is the point (0,1). 1. Find the x-coordinate of the point A in terms of a. 2. Show that for all a+0, ABP is a right angle.
Transcribed Image Text:2. Parabolic tangents and peculiar perpendicularities! a. Let la and lb be tangent lines to the parabola y=x² at x=a and x=b, respectively, where a#0. 1. For what values of a and b are la and lb perpendicular to one another? 2. Make a sketch to illustrate one case of your answer, for a=2. b. The tangent line to the parabola x2=4y at the point P(a, b) meets the line y=-1 at the point A. Suppose B is the point (0,1). 1. Find the x-coordinate of the point A in terms of a. 2. Show that for all a+0, ABP is a right angle.
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