Chapter 16.6, Problem 22E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find a parametric representation for the surface.

**22.** The part of the ellipsoid *x*^{2} + 2*y*^{2} + 3*z*^{2} = 1 that lies to the left of the *xz*-plane

To determine

**To find:** The parametric representation for part of the ellipsoid
*xz*-plane.

Explanation

**Given data:**

The equation of the ellipsoid is
*xz*-plane.

Consider *x* and *z* as parameters and parameterize the equation of ellipsoid as follows.

Rewrite the equation of ellipsoid

As the required part of the ellipsoid lies to the left of the *xz*-plane, the parameter of *y* must be a negative value

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