Chapter 13 - Vector Geometry - 13.6 A Survey of Quadratic Surfaces - Exercises - Page 692: 6

Hyperboloid of two sheets.

The equation $$ x^2-3y^2-9z^2=1$$ can be rewritten in the form $$ x^2- \frac{y^2}{1/3}-\frac{z^2}{1/9}=1\\ \frac{y^2}{1/3}+\frac{z^2}{1/9}=x^2-1 .$$ Hence the equation is a hyperboloid of two sheets (see equations on page 688).