Chapter 16.6, Problem 59E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Show that the parametric equations *x* = *a* sin *u* cos *v*, *y* = *b* sin *u* sin *v*, *z* = *c* cos *u*, 0 ⩽ *u* ⩽ π, 0 ⩽ *v* ⩽ 2π, represent an ellipsoid.

(b) Use the parametric equations in part (a) to graph the

(c) Set up, but do not evaluate, a double integral for the surface area of the ellipsoid in part (b).

**(a)**

To determine

**To show:** The parametric equations

Explanation

**Given data:**

The parametric equations are given as follows.

**Formula used:**

Write the expression for equation of ellipsoid.

Here,

Write the parametric equations as follows.

Rewrite the parametric equations as follows.

Take square and add the expressions as follows.

Simplify the expression as follows

**(b)**

To determine

**To draw:** The graph of an ellipsoid with the parametric equations

**(c)**

To determine

**To find:** The expression for surface area of the ellipsoid with the parametric equations

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