Answer
Elliptic cone, with x as the axis.
Work Step by Step
Comparing the form of the equation with Table 1 in 12-6, we find:
Cone
$\displaystyle \frac{z^{2}}{c^{2}}=\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$
Horizontal traces are ellipses (z is the axis).
Vertical traces in the planes $x=k$ and $y=k$ are hyperbolas if $k\neq 0$ but are pairs of lines if $k=0.$
Here
$x^{2}=y^{2}+4z^{2},$
so, traces in the planes $x=k$ are ellipses, (axis is the x-axis) and in the planes $y=k$ and $z=k$ are hyperbolas.
