## Thomas' Calculus 13th Edition

Published by Pearson

# Chapter 12: Vectors and the Geometry of Space - Section 12.6 - Cylinders and Quadric Surfaces - Exercises 12.6 - Page 732: 22

#### Answer

Elliptical paraboloid.

#### Work Step by Step

Rewrite as $\displaystyle \frac{z-8}{-1}=\frac{x^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}$ We compare with Table 12.1 and conclude that this is an elliptical paraboloid. It opens down and the vertex is raised up 8 units (from the origin). The traces in xz and yz planes are parabolas. The traces in planes parallel to the xy plane are circles (special case of ellipses).

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