   Chapter 16.6, Problem 22E

Chapter
Section
Textbook Problem

Find a parametric representation for the surface.22. The part of the ellipsoid x2 + 2y2 + 3z2 = 1 that lies to the left of the xz-plane

To determine

To find: The parametric representation for part of the ellipsoid x2+2y2+3z2=1 that lies to the left of the xz-plane.

Explanation

Given data:

The equation of the ellipsoid is x2+2y2+3z2=1 and it lies to the left of the xz-plane.

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

Rewrite the equation of ellipsoid x2+2y2+3z2=1 as follows.

2y2=1x23z2y2=1x23z22y2=12(1x23z2)y=±12(1x23z2)

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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