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: 35

Answer

Elliptical paraboloid
1577317359

Work Step by Step

Comparing to Table 12.1, we recognize the form of an Elliptical paraboloid (with y and z interchanged; y is negative). This means that it opens along the y-axis (instead of the z-axis), and the minus tells us that it opens in the -y direction. The cross sections with $x=k$ and $z=k$, are parabolas, and with $y= -k$ they are circles (special cases of parabolas).
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.