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