Sketching for isotherms $T(x, y) = \text{ const}$ Hi I came across this question 

Let the temperature $$T(x,y) = 4x^2+16y^2$$ in a body be independent of $z$, identify the isotherms $T(x, y) = \text{ const}$. Sketch it.

I do not understand the question. What type of equation(s) do I have to sketch?

You have to sketch
$$4x^2+16y^2=c, \text{ where $c>0$ is a constant number.}$$
that is equivalent to
$$\frac{x^2}{(\sqrt{c}/2)^2}+\frac{y^2}{(\sqrt{c}/4)^2}=1$$
which is an ellipse.
If $c=0$ you just have one point which is $(x,y)=(0,0)$.
If $c<0$ we don't have any isotherm.
