## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 13 - Vector Geometry - 13.6 A Survey of Quadratic Surfaces - Exercises - Page 693: 39

#### Answer

$$\left(\frac{x}{2}\right)^{2}+\left(\frac{y}{4}\right)^{2}+\left(\frac{z}{6}\right)^{2}=1.$$

#### Work Step by Step

By observing Figure 15(A), we get that $$a=2, \quad b=4, \quad c=6.$$ Using the equation of the ellipsoid (page 691) and the above variables, we get: $$\left(\frac{x}{2}\right)^{2}+\left(\frac{y}{4}\right)^{2}+\left(\frac{z}{6}\right)^{2}=1.$$

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