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: 2



Work Step by Step

The equation of a hyperboloid 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 hyperboloid becomes $$ \left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}=\left(\frac{z_0}{c}\right)^{2}+1$$ which represent an ellipse. So the statement is false.
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