Answer
Hyperbolic Paraboloid
Work Step by Step
We can rewrite the equation as:
$x=y^{2}- z^{2}$
$\implies \dfrac{x}{1}=\dfrac{y^{2}}{1}-\dfrac{z^{2}}{1^2}$
Compare the above equation with
$ \dfrac{z}{c}=\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}$
we find that we have a Hyperbolic Paraboloid
When $z=k$, traces are parallel to the xy-plane as parabolas opening in the $+x$ direction.
Traces are parallel to the yz-plane as hyperbolas when $x=k$.
Traces are parallel to the xz-plane as parabolas opening in the $-x$ direction when $y=k$.
