Answer
Hyperboloid of two sheets
Work Step by Step
Rewrite as:
$-x^2+y^2-4z^2=4 \implies \dfrac{-x^2}{4}+\dfrac{y}{4}-z^2=1$
On comparing the above form, we find that we have:
Hyperboloid of two sheets
$ \dfrac{-x^2}{a^2} -\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}=1$
We see that traces in planes y=k are ellipses parallel to the xy-plane and traces in x=k and y=k are parabolas parallel to the yz-plane.
