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 - Preliminary Questions - Page 692: 1



Work Step by Step

The equation of an ellipsoid is $ \left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}+\left(\frac{z}{c}\right)^{2}=1$ and to find the trace we freeze one of the three variables for example $ z=z_0$, then the equation of the ellipsoid becomes $$ \left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}=1-\left(\frac{z_0}{c}\right)^{2}$$ which represents an ellipse. However, we can also trace a single point. For example: ($x=0,y=0,z=c$) Thus, not all traces are ellipses.
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