Answer
Hyperbolic Paraboloid
Work Step by Step
Rewrite as:
$2y=2z^{2}-x^{2}$
$\displaystyle \frac{y}{1}=\frac{z^{2}}{1}-\frac{x^{2}}{2}$
On comparing the above form, we find that we have a Hyperbolic Paraboloid
$ \dfrac{z}{c}=\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}$
When $z=k$, traces are parabolas opening in the $-y$ direction and when $x=k$, traces are parabolas opening in the $+y$ direction.
