Answer
Hyperboloid of one sheet.
See image:
.
Work Step by Step
Rewriting, we get:
$\displaystyle \frac{x^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}-\frac{z^{2}}{1^{2}}=1\qquad$
which is of the form of a hyperboloid of one sheet (compare to Table 11.1 and interchange x and z).
It opens along the x-axis.
In planes parallel to the yz plane ($x=k)$, the cross sections are circles. At $x=0$, the radius is 1; at $x=\pm 2$, the radius is $\sqrt{5}$ (use this for sketching).
The cross-sections with planes parallel to xy and xz are hyperbolas.
