Chapter 13.1, Problem 43E

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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.

**43.** The cone
*y*

To determine

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

Explanation

**Given data:**

The equations of cone is

**Definition:**

Consider parametric equations as

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

Here,

*x*, *y*, and *z* are parametric equations of space curve ** C**.

Write the equation for surface of cone.

Substitute
*z*,

Apply square on both sides of equation.

Consider parametric equation

Substitute *t* for *x* in equation (2),

Write the equation for surface of plane

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