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.`

Find the equation of the circle passing through the points of intersection of the circles x^(2) + y^(2) - x + 7y - 3 = 0, x^(2) + y^(2) - 5x - y + 1 = 0 and having its centre on the line x+y = 0.

Find the equation of the circle passing through the points of intersection of the circles x^(2)+y^(2)-8x-6y-21=0 x^(2)+y^(2)-2x-15=0and(1,2)

The equation of the circle passing through (1,2) and the points of intersection of the circles x^2+y^2-8x-6y+21=0 and x^2+y^2-2x-15=0 is

The equation of the circle passing through (1,2) and the points of intersection of the circles x^2+y^2-8x-6y+21=0 and x^2+y^2-2x-15=0 is

Find the equation of the circle which passes through the points of intersection of the circle x^(2) + y^(2) + 4(x+y) + 4 = 0 with the line x+y+2 = 0 and has its centre at the origin.

Find the equation of the circle through the point of intersection of circles x^2+y^2-6x=0 and x^2+y^2+4y-1=0 and the point (-1, 1).