   Chapter 2, Problem 10P ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) The figure shows an isosceles triangle ABC with ∠ B = ∠ C. The bisector of angle B intersects the side AC at the point P. Suppose that the base BC remains fixed but the altitude |AM | or the triangle approaches 0, so A approaches the midpoint M or BC. What happens to P during this process? Does it have a limiting position? If so, find it.(b) Try to sketch the path out by P during this process. Then find an equation of this curve and use this equation to sketch the curve.

(a)

To determine

To find: The position of the point P in the given process and to check whether P have a limiting position.

Explanation

Graph:

Calculation:

Let the coordinate system and drop a perpendicular from P.

From the triangle ΔNCP the angle NCP that tan(2θ)=y1x,

And from the triangle ΔNBP the angle NBP that tan(θ)=yx.

By using double-integral formula for tangents,

y1x=tan(2θ)b±b24ac2ay1x=2tanθ1tan2θy1x=2(yx)1(yx)2y1x=2yx1y2x2

Simplifying above equation

y1x=

(b)

To determine

To find: The equation of the curve and sketch the path traced out by P.

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