## 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: 33

#### Answer

Hyperbollic paraboloid

#### Work Step by Step

Rewriting, $\displaystyle \qquad \frac{z-1}{1}=\frac{y^{2}}{1^{2}}-\frac{x^{2}}{1^2}$ and comparing to Table 12.1, we recognize the form of a Hyperbollic paraboloid, with the "saddle" raised up by unit (in the z direction). The cross sections with planes $x=k , y=k$ are parabolas, and the cross section with planes $z=k$ are hyperbolas.

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