Solve the Problem $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$

Solve the problem.
-Recall that an equation of a circle can be written in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ , where $( h , k )$ is the center and $r$ is the radius. Expanding terms, the equation can also be written in the form $x ^ { 2 } + y ^ { 2 }$ $+ A x + B y + C = 0$ .
a . Find an equation of the form $x ^ { 2 } + y ^ { 2 } + A x + B y + C = 0$ that represents the circle that passes through the three points $( 4 , - 4 ) , ( 2 , - 8 )$ , and $( - 5 , - 1 )$ .
b. Find the center and radius of the circle.

A) a. $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 8 = 0$
b. Center: $( 1,4 )$ ; Radius: 4

B) a. $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 8 = 0$
b. Center: $( - 1 , - 4 )$ ; Radius: 5

C) a. $x ^ { 2 } + y ^ { 2 } + 2 x + 8 y - 8 = 0$
b. Center: $( 1,4 )$ ; Radius: 4

D) a. $x ^ { 2 } + y ^ { 2 } + 2 x + 8 y - 8 = 0$
b. Center: $( - 1 , - 4 )$ ; Radius: 5