Example 6. Find the level curves of the function $z=x y$.
Solution. A level line of the function $z=f(x, y)$ is the geometric locus of points in the plane $O x y$ for which the given function has the same value: the equation of the level line is

$$
f(x, y)=c
$$

In this case, we have $x y=c$. The level lines are hyperbolas when $c \neq 0$.