The circle `x^2 + y^2 - 2x - 4y + 1 = 0` and `x^2 + y^2 + 4x + 4y - 1 = 0`

Find the equation of the circle which passes through (1, 1) and cuts orthogonally each of the circles x^2 + y^2 - 8x - 2y + 16 = 0 and x^2 + y^2 - 4x -4y -1 = 0

A circle through the common points of the circles x^(2) + y^(2) - 2x - 4y + 1 = 0 and x^(2) + y^(2) - 2x - 6y + 1 = 0 has its centre on the line 4x - 7y - 19 = 0 . Find the centre and radius of the circle .

Find the equation of the circles which passes through the origin and the points of intersection of the circles x^(2) + y^(2) - 4x - 8y + 16 = 0 and x^(2) + y^(2) + 6x - 4y - 3 = 0 .

The circle x^2 + y^2 - 8x + 4y +4 = 0 touches

Prove that the centres of the three circles x^(2) + y^(2) - 2x + 6y + 1 = 0, x^(2) + y^(2) + 4x - 12y + 9 = 0 and x^(2) + y^(2) - 16 = 0 are collinear.

Prove that the radii of circles x^2 + y^2 = 1, x^2 + y^2 - 2x -6y = 6 and x^2 + y^2 - 4x - 12y = 9 are in A.p.

Find the equation to the common chord of the two circles x^(2) + y^(2) - 4x + 6y - 36 = 0 and x^(2) + y^(2) - 5x + 8y - 43 = 0 .

Prove that the centres of the circles x^(2) + y^(2) - 10x + 9 = 0, x^(2) + y^(2) - 6x + 2y + 1 = 0 and x^(2) + y^(2) - 18x - 4y + 21 = 0 lie on a line, find the equation of the line on which they lie.

Let P be the point on the parabola, y^2=8x which is at a minimum distance from the centre C of the circle, x^2+(y+6)^2=1. Then the equation of the circle, passing through C and having its centre at P is : x^ 2 + y^ 2 − x + 4 y + 12 = 0 x^ 2 + y^ 2 − x/ 4 + 2 y − 24 = 0 x^ 3 + y^ 2 − 4 x + 9 y − 18 = 0 x^ 2 + y^ 2 − 4 x + 8 y + 12 = 0

The circle x^(2) + y^(2) + 2x - 4y - 11 = 0 and the line x-y+1=0 intersect at A and B. Find the equation to the circle on AB as diameter.