University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.6 - Cylinders and Quadric Surfaces - Exercises - Page 636: 27

Answer

Hyperboloid of one sheet. See image: .

Work Step by Step

Comparing to table Table 11.1, the equation is of form $\displaystyle \frac{x^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}-\frac{z^{2}}{1^{2}}=1\qquad$ which 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 this for sketching). The cross-sections with planes parallel to xz and yz are hyperbolas.
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