Answer
Hyperboloid of one sheet,
Work Step by Step
Rewriting,
$\displaystyle \frac{z^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}-\frac{x^{2}}{1^{2}}=1\qquad$
this is of the form of a hyperboloid of one sheet,
(compare to Table 12.1 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 and at $x=\pm 2$, the radius is $\sqrt{5}$ (use for sketching).
The cross sections with planes parallel to xy and xz are hyperbolas.
