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: 24


Elliptical paraboloid

Work Step by Step

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