Example 2. Find the level surfaces of the scalar field

$$
u=x^{2}+y^{2}-z^{2}
$$
Solution. Level surfaces are defined by the equation

$$
x^{2}+y^{2}-z^{2}=C, \text { where } C=\text { const. }
$$

When $C=0$, we obtain a circular cone. For any $C>0$, we obtain one-sheet hyperboloids of rotation with the axis coinciding with the $Oz$ axis. When $C<0$, we obtain a two-sheet hyperboloid of rotation.