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: 34

Answer

Elliptical (circular) cone.
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Work Step by Step

Dividing with 4, we rewrite the equation as: $\displaystyle \frac{x^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}=\frac{z^{2}}{2^{2}}$ and comparing to Table 12.1, we recognize the form of an Elliptical cone. The cross sections with planes $z=k$ are circles (at $z=\pm 2, $ the radius is 1). Circles are special cases of ellipses.
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