## 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: 31

#### Answer

Hyperbollic paraboloid.

#### Work Step by Step

The form of the equation is $\displaystyle \frac{y^{2}}{1^{2}}-\frac{x^{2}}{1^{2}}=\frac{z}{1},\quad$ which is a Hyperbollic paraboloid (when comparing to Table 12.1). 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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