Find the equations of the circles which pass through the common points of the following pair of circles. `x^2 + y^2 + 2x + 3y – 7 = 0`

Find the equations of the circles which pass through the common points of the following pair ofcircles.(a)x^(2)+y^(2)+2x+3y-7=0 and x^(2)+y^(2)+3x-2y-1=0 through the point (1,2)

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 which passes through the point (1, 1) & which touches the circle x^(2) + y^(2) + 4x – 6y – 3 = 0 at the point (2, 3) on it.

Find the equation of the circle which passes through the point (2,0), (0,2) and orthogonally to the circle 2x^2 + 2y^2 + 5x - 6y + 4 = 0 .

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.

Show that the circle x^(2) + y^(2) + 4(x+y) + 4 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x+y+2 = 0 and which also passes through the origin.

Show that the circle x^(2) + y^(2) + 6(x-y) + 9 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x-y+4 = 0 and which also passes through the origin.

Find the equation of the circle which passes through the points (2,0)(0,2) and orthogonal to the circle 2x^2+2y^2+5x-6y+4=0 .

Find the equation of the circle which passes through the points (2,0)(0,2) and orthogonal to the circle 2x^2+2y^2+5x-6y+4=0 .

Find the equation of the common chord of the following pair of circles. x^2 + y^2 + 3y+ 1 = 0 , x^2 + y^2 + 4x + 3y + 2 = 0 .