Answer
Ellipsoid
Work Step by Step
Here, we have: $4x^2+4y^2-8y+z^2=0$
Rewrite as:
$4x^2+4(y^{2}-2y) + z^{2} =0$
or, $4x^2 +4(y^2-2y+1) +z^2=4$
or, $x^2+(y-1)^2 + \dfrac{z^2}{4}=1$
On comparing the above form with
$ \dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}+\dfrac{z^2}{c^2}=1$
we find that we have an ellipsoid.
