Identify the surface defined by the following equation.

$x^2+y^2+9z^2+2x=0$

Select the correct choice below and fill in the answer boxes to complete your choice.

A$.$ The surface defined by the equation is a hyperboloid of two sheets centered at $$ and whose traces in planes parallel to the xy$-$plane are ellipses. The shortest distance between the two sheets is $$

B$.$ The surface defined by the equation is a hyperboloid of one sheet centered at $(,.$ and is centered around the $z-$axis. In the xy$-$plane, the trace has length $$ in the $x-$direction and length $$ in the $y-$direction.

C$.$ The surface defined by the equation is an elliptic cone centered at $(.-)$ and whose traces in planes parallel to the xy$-$plane are ellipses.

D$.$ The surface defined by the equation is an ellipsoid centered at $(-1,0,0)$ that has length $2$ in the $x-$direction, $2^T$ in the $y-$direction, and $\frac{2}{3}$ in the $z-$direction.