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: 11

Answer

Hyperbolic paraboloid

Work Step by Step

The equation $$ z=3x^2-7y^2$$ can be rewritten as follows $$ z=\left(\frac{x}{1/\sqrt 3}\right)^{2}-\left(\frac{y}{1/\sqrt{7}}\right)^{2} $$ which is an equation of a hyperbolic paraboloid with $ a=1/\sqrt{ 3}, b=1/\sqrt{7}$ (see equations on page 691).
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