The equation of circle passing through the intersection points of the circles
x² + y² - 2x - 6y + 9 = 0 and
x^2 + y^2 - 4x - 8 y + 11 = 0 which also passes through origin is
The circles are
(x-1)^2 + (y-3)^2 = 1
(x-2)^2 + (y-4)^2 = 9
combine them to get
9(x-1)^2 + 9(y-3)^2 = (x-2)^2 + (y-4)^2
x = (7±3√2)/8
y = 23/8
Now you have three points, so you can solve as you did in the other post.