Answer
Hyperbolic Paraboloid,
center: origin,
Traces in y=k are hyperbolas.
Traces in x=k, z=k are parabolas.
Work Step by Step
Rewrite:
$2y=2z^{2}-x^{2}$
$\displaystyle \frac{y}{1}=\frac{z^{2}}{1}-\frac{x^{2}}{2}$
Comparing the form to Table 1, we find:
Hyperbolic Paraboloid
$\displaystyle \frac{z}{c}=\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}},\quad $where
Horizontal traces (z=k) are hyperbolas.
Vertical traces (x=k, y=k) are parabolas.
