Answer
Ellipsoid.
Work Step by Step
The equation
$$ x^2+3y^2+9z^2=1$$
can be rewritten in the form
$$ x^2+ \frac{y^2}{1/3}+\frac{z^2}{1/9}=1.$$
Hence the equation is an an ellipsoid (see equations on page 687).
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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: 3
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