Chapter 16.6, Problem 23E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find a parametric representation for the surface.

**23.** The part of the sphere *x*^{2} + *y*^{2} + *z*^{2} = 4 that lies above the cone

To determine

**To find:** The parametric representation for part of the sphere

Explanation

**Given data:**

The equation of the sphere is

Consider *x* and *y* as parameters and parameterize the equation of sphere as follows.

Rewrite the equation of sphere

As the required part of the sphere lies above the cone
*z* must be a positive value.

Therefore, the parameters of part of the sphere

The limit of the parameters is determined as follows.

Consider the equation of sphere as follows.

Write the equation of cone that intersects the sphere as follows

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