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?
Let's put the circle in standard form
x^2 + 4x +y^2 -6y = 3 now 'complete the square'on x and y
(x+2)*2 + (y-3)^2 = 3 +4+9
(x+2)^2 + (y-3)^2 = 4^2 so the center is (a,b) = (-2,3) and the radius is 4 a+b+r = 5