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 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

The circle through (-2,5),(0,0) and intersecting the circle x^(2)+y^(2)-4x+3y-1=0 orthogonally is

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

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

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 circle passing through the points (-2, 5), (0, 0) and intersecting x^2+y^2-4x+3y-2=0 orthogonally is

Find the equation of the circle passing through the origin, having its centre on the line x+y=4 and intersecting the circle x^2+y^2-4x+2y+4=0 orthogonally.

Find the equation of the circle passing through the origin, having its centre on the line x+y=4 and intersecting the circle x^2+y^2-4x+2y+4=0 orthogonally.