   Chapter 11.3, Problem 69E

Chapter
Section
Textbook Problem

# Using Points of Intersection In Exercises 65–68, (a) find all points of intersection of the graphs of the two equations, (b) find the unit tangent vectors to each curve at their points of intersection, and (c) Find the angle ( 0 0 ≤ θ ≤ 90 0 ) between the curves at their point of intersection. y = 1 − x 2 , y = x 2 − 1

(a)

To determine

To calculate:

All points of intersection of the graphs of the two equations

Explanation

Given:

y=1x2,y=x21

Calculation:

Perform the following steps to plot the graph:

Perform the following steps to plot the graph:

1

(b)

To determine

To Calculate:

The unit tangent vectors to each curve at their point of intersection

(c)

To determine

To Calculate:

The angle between the curves at their point of intersection

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