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

Answer

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.