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: 29


Hyperboloid of two sheets.

Work Step by Step

Rewriting the equation, $\displaystyle \frac{z^{2}}{1^{2}}-\frac{x^{2}}{1^{2}}-\frac{y^{2}}{1^{2}}=1\quad$ and comparing to Table 12.1, we recognize the form of a Hyperboloid of two sheets, which: - opens along the z-axis, - has cross sections with planes $z=k$ as circles. At $z=\pm 3$ the radius is $\sqrt{3^{2}-1}=\sqrt{8}$. - has cross sections with planes parallel to $x=0$ and $y=0$ as hyperbolas.
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