For what value of c will the circle with equation x^2 + 6x + y^2 - 14y + c = 0 have a radius of length 4?
x^2 + 6x + y^2 - 14y = -c complete the square on x,y
x^2 + 6x + 9 + y^2 - 14y + 49 = -c + 9 + 49
To have a radius of 4
-c + 9 + 49 must = 16
So
-c = 16 - 9 - 49
-c = -24
c = 24
