Answer
Hyperboloid of one sheet.
Work Step by Step
The equation can be rewritten in the form
$$
\left(\frac{x}{3}\right)^{2}-\left(\frac{y}{4}\right)^{2}+\left(\frac{z}{1/\sqrt{2}}\right)^{2}=1
$$
which is a hyperboloid of one sheet.
(See equations on page 691-692.)
