For what value of c will the circle with equation x^2 + 6x + y^2 - 4y + c = 0 have a radius of length 4?
x^2 + 6x + y^2 - 4y = -c complete the square on x and y
x^2 + 6x + 9 + y^2 - 4y + 4 = -c + 9 + 4
To have a radius of 4....then
-c + 9 + 4 = 4^2
-c + 9 + 4 = 16
-c + 13 = 16
-c = 16 - 13
-c = 3
c = -3
+20 
