University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.6 - Cylinders and Quadric Surfaces - Exercises - Page 636: 32

Answer

Hyperbollic paraboloid. See image: .

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. (Compare to Table 11.1, with x and y interchanged.) The cross-sections with planes $x=k, y=k$ are parabolas; the cross-section with planes $z=k$ are hyperbolas.
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