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: 27

Answer

Hyperboloid of one sheet,
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Work Step by Step

Comparing to table Table 12.1, the equation is of the form $\displaystyle \frac{x^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}-\frac{z^{2}}{1^{2}}=1\qquad$ this is a hyperboloid of one sheet, that opens along the z-axis. The cross-sections with planes parallel to xy are circles (ellipse, special case). At z=0, the radius is 1, at $z=\pm 2$, the radius is $\sqrt{5}$ (use for sketching). The cross sections with planes parallel to xz and yz are hyperbolas.
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