Answer
Elliptic Cone
Work Step by Step
Re-write as:
$\displaystyle \frac{y^{2}}{1^{2}}=\frac{x^{2}}{1^{2}}+\frac{z^{2}}{3^{2}}$
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. Here, we have the y-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.
Traces in the y=k planes are ellipses parallel to the xz-plane.
