Answer
See image:
Work Step by Step
The level curves (isothermals) have the form:
$k=\displaystyle \frac{100}{(1+x^{2}+2y^{2})}$
$1+x^{2}+2y^{2}=\displaystyle \frac{100}{k}$
$x^{2}+2y^{2}=\displaystyle \frac{100}{k}-1 $, a family of ellipses
(Graphed with geogebra)