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: 21

Answer

Elliptical paraboloid.
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Work Step by Step

Divide with 4, $\displaystyle \frac{z}{4}=\frac{x^{2}}{2^{2}}+\frac{y^{2}}{1^{2}}$ Compare with Table 12.1 and conclude that this is an elliptical paraboloid. The traces in xz and yz planes are parabolas. The traces in planes parallel to the xy plane are ellipses.
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