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


Elliptical paraboloid

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).
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