Answer
Elliptic Cone
Work Step by Step
We can re-write the equation as:
$\displaystyle \dfrac{x^{2}}{2^2}=\dfrac{y^2}{1^{2}}+\dfrac{z^{2}}{2^{2}}$
We have the equation of an Elliptic Cone along the x-axis with (0,0,0) as the vertex.
The 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 xz plane respectively.
The traces in the y=k planes are hyperbolas that open in the $\pm x$-axis, parallel to the xz-plane.
