Identify the surface defined by the following equation. \[ x^{2}+y^{2}+8 z^{2}+10 x=-24\] Select the correct choice below and fill in the answer boxes to complete your choice. A. The surface defined by the equation is an elliptic cone centered atI and whose traces in planes parallel to the \( x y \)-plane are ellipses. B. The surface defined by the equation is an ellipsoid centered at ,that has length in the x -direction, in the \( y \)-direction, and in the \(\mathbf{z}\)-direction. C. 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 D. The surface defined by the equation is a hyperboloid of one sheet centered at ,,\(\square \) 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.