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: 23

Answer

See image: .

Work Step by Step

Subtract 4 and divide with (-4) $\displaystyle \frac{x-4}{-4}=\frac{y^{2}}{1^{2}}+\frac{z^{2}}{2^{2}}$ Compare with Table 11.1 and, after interchanging x and z, conclude that this is an elliptical paraboloid, which opens toward the negative direction of x. The vertex is shifted 4 units in the +x direction. The traces in xy and xz planes are parabolas. The traces in planes parallel to the yz plane are ellipses.
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