The equation of circle passing through
intersection points of two circles is given by S₁ + lamda S₂ = 0 (where S 1 and S2 are the equations of given circle)
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
So, you just posted it again, without trying to solve it?
As it turns out, the intersection points I calculated do not in fact exist, since the two circles do not intersect at all.
See the plot at
www.wolframalpha.com/input/?i=plot+%28x-1%29%5E2+%2B+%28y-3%29%5E2+%3D+1%2C+%28x-2%29%5E2+%2B+%28y-4%29%5E2+%3D+9
So, I guess I need to figure out how I got those two points. In the meantime, maybe you should come up with circles that do in fact intersect.