The equation of the circle shown in the following diagram can be written as \(x^2 + Ay^2 + Bx + Cy + D = 0\) . Find \(A+B+C+D\).
https://latex.artofproblemsolving.com/d/4/b/d4b6468bc485090058e6cdadf256aca42c141d53.png
The center is ( -1, 1)
And the radius is √5
So....the equation is
(x + 1)^2 + (y - 1)^2 = 5 simplify
x^2 + 2x + 1 + y^2 - 2y + 1 = 5
x^2 + 1y^2 + 2x - 2y - 3 = 0
So
A + B + C + D =
1 + 2 - 2 - 3 = -2
+4609 
