The question is draw several labelled level curves for the function
$\displaystyle F(x,y)=1/(x^2+y^2)$
and sketch the graph of its surface.
Nooo idea where to start. Help!
Choose $\displaystyle c\in\mathbb{R}\Longrightarrow \frac{1}{x^2+y^2}=c\Longleftrightarrow x^2+y^2=\frac{1}{c}\Longrightarrow$ this means that it must be $\displaystyle c> 0$ (otherwise you get the empty set) , and for $\displaystyle c>0$ you get the
circle with radius $\displaystyle \frac{1}{\sqrt{c}}$ and centered at the origin . These are all the level curves.
Tonio