Answer
Hyperboloid of two sheets.
See image:
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Work Step by Step
Rewriting the equation, we get:
$\displaystyle \frac{z^{2}}{1^{2}}-\frac{x^{2}}{1^{2}}-\frac{y^{2}}{1^{2}}=1\quad$
and comparing to Table 11.1, we recognize the form of a Hyperboloid of two sheets. It has the following properties:
- opens along the y-axis,
- cross sections with planes $z=k$ are circles. At $z=\pm 3$ the radius is $\sqrt{3^{2}-1}=\sqrt{8}$.
- cross sections with planes parallel to $x=0$ and $y=0$ are hyperbolas.
