Answer
Hyperbollic paraboloid
Work Step by Step
Rewriting, $\displaystyle \qquad \frac{z-1}{1}=\frac{y^{2}}{1^{2}}-\frac{x^{2}}{1^2}$
and comparing to Table 12.1, we recognize the form of
a Hyperbollic paraboloid, with the "saddle" raised up by unit (in the z direction).
The cross sections with planes $x=k , y=k$ are parabolas,
and the cross section with planes $z=k$ are hyperbolas.
