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: 22

Answer

Elliptical paraboloid.
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Work Step by Step

Rewrite as $\displaystyle \frac{z-8}{-1}=\frac{x^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}$ We compare with Table 12.1 and conclude that this is an elliptical paraboloid. It opens down and the vertex is raised up 8 units (from the origin). The traces in xz and yz planes are parabolas. The traces in planes parallel to the xy plane are circles (special case of ellipses).
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