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: 30

Answer

Hyperboloid of two sheets

Work Step by Step

The equation has the form a Hyperboloid of two sheets, as found in Table 12.1, with variables y and z interchanged. The hyperboloid opens along the y-axis. Cross sections with planes $y=k$ are ellipses. Cross sections with planes parallel to $x=0, z=0$, are hyperbolas.
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