It is generally hard to draw a picture of the graph of a function of two variables. Sometimes, we need to draw
*level curves*; just remember the level curves on a map, in geography.

Take a function *f* of two variables *x* and *y*, defined on a doamin *D*. For a real number *k*, the curve of
level *k*, denoted
is the set of all the points in *D* such that *f*(*x*,*y*)=*k*.

- If
*k*< 0, then is empty. - contains a single point, namely the origin.
- If
*k*>0, then is a circle centerd at the origin and whose radius is equal to .