Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.6 A Survey of Quadratic Surfaces - Exercises - Page 692: 14


Ellipsoid; there is no trace with $ y=5$.

Work Step by Step

The equation $$ x^2+ \left(\frac{y}{4}\right)^{2} +z^2=1 $$ is an ellipsoid. (See equations on page 691.) To find the trace with the plane $ y=5$, we have $$ x^2+ 25/16+z^2=1\Longrightarrow x^2+ z^2=-9/16$$ which is impossible and hence there is no trace with $ y=5$.
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