Identify the surface defined by the following equation.

$-x^2-y^2+\frac{z^2}{16}+8x-10y=45$

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

A$.$ 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 $z-$direction.

B$.$ The surface defined by the equation is a hyperboloid of one sheet centered at $1,$