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

question 49

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 \(= 7\)