Answer
See image:
Work Step by Step
Level curves have the form:
$\ln(x^{2}+4y^{2})=k$
$x^{2}+4y^{2}=e^{k}$
Graphing,
$4y^{2}=e^{k}-x^{2}$
$y^{2}=\displaystyle \frac{e^{k}-x^{2}}{2}$
$y=\pm\sqrt{\frac{e^{k}-x^{2}}{2}}$
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 14 - Partial Derivatives - 14.1 Exercises - Page 914: 46
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