Chapter 13.1, Problem 45E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find a vector function that represents the curve of intersection of the two surfaces.

**45.** The hyperboloid *z* = *x*^{2} − *y*^{2} and the cylinder *x*^{2} + *y*^{2} = 1

To determine

**To find**: the vector function of a curve that intersects two surfaces.

Explanation

**Given data:**

The equation of the hyperboloid is

**Definition:**

Consider parametric equations as

Write the expression for vector function in terms of parametric equations.

Here,

Modify equation (1) as follows.

The surface equation
*z*-plane is at

Write the expression for surface of cylinder.

Substitute
*x* and
*y*,

The RHS is equal to the LHS

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