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: 28


Hyperboloid of one sheet,

Work Step by Step

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