Coordinate geometry question (1 Viewer)

[bic]

anybody got any ideas on how to go about this one..

show that every circle that passes through the intersections of the circle x^2 + y^2 = 2 and the straight line y = x can be written in the form (x-h)^2 + (y+h)^2 = 2(1+h^2)

thanks

 

[Estel]

x^2 + y^2 - 2 = 0
y - x = 0

Intersection:
x^2 + y^2 - 2 + 2h(y-x) = 0, for some constant h.
(x-h)^2 - h^2 + (y+h)^2 - h^2 - 2 = 0
(x-h)^2 + (y+h)^2 = 2(1+h^2)