Hyperboloid of two sheets

Hyperboloid of two sheets

The hyperboloid of two sheets does not contain lines. The discussion of plane sections can be performed for the unit hyperboloid of two sheets with equation $${\displaystyle H_{2}:\ x^{2}+y^{2}-z^{2}=-1.}$$ which can be generated by a rotating hyperbola around one of its axes (the one that cuts the hyperbola)