Chapter 13.1, Problem 44E

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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.

**44.** The paraboloid z = 4*x*^{2} + *y*^{2} and the parabolic cylinder *y* = *x*^{2}

To determine

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

Explanation

**Given data:**

The equations of paraboloid 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**.

The equation
*xy*-plane and *z*-plane is

Substitute *t* for *x* in equation

Write the expression for surface of a paraboloid

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