Answer
Ellipsoid
Work Step by Step
Given: $2r^2+z^2=1$
We know that $r^2=x^2+y^2 \implies r=\sqrt{x^2+y^2}$
Thus, we have
$2r^2+z^2=1$
This can be written as:
$2(x^2+y^2)+z^2=1$
or, $2x^2+2y^2+z^2=1$
Thus, the surface is an Ellipsoid.
Multivariable Calculus, 7th Edition
by Stewart, James
Published by
Brooks Cole
ISBN 10:
0-53849-787-4
ISBN 13:
978-0-53849-787-9
Chapter 15 - Multiple Integrals - 15.8 Exercises - Page 1055: 8
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