If $$y=2 x$$ is a chord of circle $$x^2+y^2-10 x=0$$, then the equation of circle with this chord as diameter is

Equationof the chord of the circle $$x^2+y^2-4 x-10 y+25=0$$ having mid-point $$(1,2)$$ is

The equation of common tangent to the circles $$x^2+y^2-4 x+10 y+20=0$$ and $$x^2+y^2+8 x-6 y-24=0$$ is

If a circle passes through the points $$(0,0),(x, 0)$$ and $$(0, y)$$, then the coordinates of its centre are