University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.6 - Cylinders and Quadric Surfaces - Exercises - Page 636: 24

Answer

Elliptical paraboloid See image: .

Work Step by Step

Subtract 1 and divide with (-1) $\displaystyle \frac{y-1}{-1}=\frac{x^{2}}{1^{2}}+\frac{z^{2}}{2^{2}}$ Compare with Table 11.1 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 units 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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