The locus of the centre of the circle passing through the intersection of the circles `x^2+y^2= 1` and `x^2 + y^2-2x+y=0` is

Show that the locus of the centres of the circles passing through the points of intersections of the circles x^2+y^2=1 and x^2+y^2-2x+y=0 is x+2y=0

The locus of the centres of the circles passing thorugh the points of intersection of the circles x^(2) + y^(2) =1 and x^(2) + y^(2) - 2x +y=0 is

Find the equation of the circle passing through the intersection of the circles, x^2+y^2-2ax=0 and x^2+y^2-2by=0 and having the centre on the line x/a - y/b = 2.

The radius of the circle passing through the points of intersection of ellipse x^2/a^2+y^2/b^2=1 and x^2-y^2 = 0 is

Find the equation of the circle passing through the intersection of the circles x^2+y^2=2ax, x^2+y^2=2by and having its centre on the line x/a-y/b=2 .

The locus of the centres of circles passing through the origin and intersecting the fixed circle x^(2)+y^(2)-5x+3y-1=0 orthogonally is

The locus of the centres of circles passing through the origin and intersecting the fixed circle x^(2)+y^(2)-5x+3y-1=0 orthogonally is