Answer
Elliptic Cone
Work Step by Step
Re-write the equation as:
$\displaystyle \frac{x^{2}}{2^2}=\frac{y^2}{1^{2}}+\frac{z^{2}}{2^{2}}$
or, $\displaystyle \frac{y^{2}}{1}=\frac{x^{2}}{1}+\frac{z^{2}}{9}$
We see that we have the equation of an Elliptic Cone along the x-axis. Thus, we have the x-axis as the axis, and (0,0,0) as the vertex.
Traces in the planes x=k and z=k are hyperbolas for $k\neq 0$, and straight lines for k=0, parallel to the yz-plane and the xz-plane, respectively.
Traces in the y=k planes are hyperbolas that open in the $\pm x$-axis, parallel to the xz-plane.
