Answer
Hyperboloid of two sheets.
Work Step by Step
Rewriting the equation,
$\displaystyle \frac{z^{2}}{1^{2}}-\frac{x^{2}}{1^{2}}-\frac{y^{2}}{1^{2}}=1\quad$
and comparing to Table 12.1, we recognize the form of a Hyperboloid of two sheets, which:
- opens along the z-axis,
- has cross sections with planes $z=k$ as circles. At $z=\pm 3$ the radius is $\sqrt{3^{2}-1}=\sqrt{8}$.
- has cross sections with planes parallel to $x=0$ and $y=0$ as hyperbolas.
