For what value of c will the circle with equation x^2 + 6x + y^2 - 4y - 10x - 12y + c = 0 have a radius of length 4?
Rearrange as
x^2 - 4x + y^2 - 16 y = -c complete the square on x , y
(x^2 - 4x + 4) + ( y^2 - 16y + 64 ) = -c + 4 + 64
We want
-c + 4 + 64 = r^2
-c + 68 = 4^2
-c = 16 - 68
c = 68 - 16
c = 52
c = -76.
