Find the equation of the circle passing throught (1,1) and the points of intersection of the circles `x^(2)+y^(2)+13x-3y=0` and `2x^(2)+2y^(2)+4x-7y-25=0`

Show that the equation of the circle passing through (1,1) and the points of intersection of the circles x^(2)+y^(2)+13x-13y=0 and 2x^(2)+2y^(2)+4x-7y-25=0 is 4x^(2)+4y^(2)+30x-13y-25=0

The equation of the circle passing through the origin and the points of intersection of the two circles x^(2)+y^(2)-4x-6y-3=0,x^(2)+y^(2)+4x-2y-4=0 is

Find the equation of the circle passing through the points of intersection of the circles x^(2)+y^(2)-2x-4y-4=0 and x^(2)+y^(2)-10x-12y+40=0 and whose radius is 4.

Find the equation of the circle passing through the point (2, 4) and centre at the point of intersection of the lines x-y=4 and 2x+3y=-7 .

Find the equation of the circle passing through the point of intersection of the circles x^(2)+y^(2)-6x+2y+4=0,x^(2)+y^(2)+2x-4y-6=0 and with its centre on the line y=x

The equation of the circle passing through the points of intersection of the circles x^(2)+y^(2)+6x+4y-12=0 , x^(2)+y^(2)-4x-6y-12=0 and having radius sqrt(13) is