Answer
Hyperboloid of one sheet,
Work Step by Step
Comparing to table Table 12.1, the equation is of the form
$\displaystyle \frac{x^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}-\frac{z^{2}}{1^{2}}=1\qquad$
this is a hyperboloid of one sheet, that opens along the z-axis.
The cross-sections with planes parallel to xy are circles (ellipse, special case).
At z=0, the radius is 1, at $z=\pm 2$, the radius is $\sqrt{5}$ (use for sketching).
The cross sections with planes parallel to xz and yz are hyperbolas.
