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: 23

Answer

Elliptical paraboloid
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Work Step by Step

Subtract 4 and divide with (-4) $\displaystyle \frac{x-4}{-4}=\frac{y^{2}}{1^{2}}+\frac{z^{2}}{2^{2}}$ We compare with Table 12.1 and, after interchanging x and z, conclude that this is an elliptical paraboloid, which opens toward the negative direction of x. The vertex is shifted 4 units in the +x direction. The traces in xy and xz planes are parabolas. The traces in planes parallel to the yz plane are ellipses.
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