For What Value Of $a$ Does the Equation $x ^ { 2 } + y ^ { 2 } - a x + 8 y + 16 = 0$

Multiple Choice

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 8 y + 16 = 0$ represent a circle with center $( 5 , - 4 ) ?$ When $a$ assumes this value, what is the radius of the circle?

A) $\quad a = 9 , \quad$ radius $= 6$
B) $\quad a = 10 , \quad$ radius $= 5$
C) $\quad a = 8 , \quad$ radius $= 6$
D) $\quad a = 9 , \quad$ radius $= 4$
E) $\quad a = 11$ , radius $= 7$