The equation of a circle in the coordinate plane can be written as $Ax^2 + 2y^2 + Bx + Cy = 50.$ The center of the circle is at $(-5,2)$. Let $r$ be the radius of the circle. Find A+B+C+r.
If this is a circle A must = 2
We can write
2 ( x + 5)^2 + 2(y - 2)^2 = 50 + 50 + 8
2 ( x^2 + 10x + 25) + 2(y^2 - 4y +4) = 50 + 50 + 8
2x^2 + 20x + 50 + 2y^2 - 8y + 8 = 108
A =2
B = 20
C = -8
r = sqrt (108)
A + B + C + r = 14 + sqrt (108)
+1167 
