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: 13


Eellipsoid; the trace is a circle in the $ xz $-plane.

Work Step by Step

The equation $$ x^2+ \left(\frac{y}{4}\right)^{2} +z^2=1 $$ is an ellipsoid. To find the trace in the $ xz $-plane, we put $ y=0$; hence we have $$ x^2+ z^2=1$$ which is a circle in the $ xz $-plane. (See equations on page 691.)
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