Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.6 - Cylinders and Quadric Surfaces - Exercises 12.6 - Page 732: 33

Answer

Hyperbollic paraboloid
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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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