Find the equation of the circle through points of intersection of the circle `x^2 + y^2 -2x - 4y + 4 =0 `and the line `x + 2y = 4` which touches the line `x + 2y = 0`.

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).

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

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 passing through the intersection of the circles x^2 + y^2-4 = 0 and x^2+y^2-2x-4y+4=0 and touching the line x + 2y=0

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 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 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 circle x^(2)+y^(2)-2x+4y-20=0 , the line 4x-3y-10 =0 and the point (3, 1) is