Let \(C\) be the circle with equation \(x^2-6y-3=-y^2-4x\) . If (a,b) is the center of \(C\) and \(r\) is its radius, what is the value of a+b+r?
x^2 - 6y - 3 = -y^2 - 4x rearrange as
x^2 + 4x + y^2 - 6y = 3 complete the square on x and y
x^2 + 4x + 4 + y^2 -6y + 9 = 3 + 4 + 9 factor and simplify
(x + 2)^2 + (y - 3)^2 = 16
The center is (-2, 3) and the radius = 4
So a + b + r = -2 + 3 + 4 = 5
+885 
