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

Two circles centred at $$(2,3)$$ and $$(4,5)$$ intersects each other. If their radii are equal, then the equation of the common chord is

The equation of a circle that passes through the origin and cut off intercepts $$-2$$ and 3 on the $$\mathrm{X}$$-axis and $$\mathrm{Y}$$-axis respectively is