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: 37

Answer

Hyperboloid of one sheet. See image: .

Work Step by Step

Comparing to Table 12.1, we recognize the form of a hyperboloid of one sheet, with the z-axis as the axis. The intersections with the planes parallel to the xy-plane are circles. The intersections with the planes parallel to the xz-plane are hyperbolas. The intersections with the planes parallel to the yz-plane are hyperbolas.
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