   Chapter 16.6, Problem 21E

Chapter
Section
Textbook Problem

Find a parametric representation for the surface.21. The part of the hyperboloid 4x2 − 4y2 − z2 = 4 that lies in front of the yz-plane

To determine

To find: The parametric representation of the hyperboloid 4x24y2z2=4 that lies in front of the yz-plane.

Explanation

Given:

The equation of the hyperboloid is 4x24y2z2=4 and it lies in front of the yz-plane.

Calculation::

Consider y and z as parameters that parameterize the equation of hyperboloid as follows.

Rewrite the equation of hyperboloid 4x24y2z2=4 as,

4x2=4+4y2+z2x2=4+4y2+z24x2=1+y2+14z2x=±1+y2+14z2

As the hyperboloid is in front of the yz-plane, the parameter x must be a positive value

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