The centres of the circles `x ^(2) + y ^(2) =1, x ^(2) + y^(2)+ 6x - 2y =1 and x ^(2) + y^(2) -12 x + 4y =1` are

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

The centre of the circle x^(2)+y^(2)-6x+4y-1=0 is

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.

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

Prove that the centres of the circle x^(2) + y^(2) - 4x - 2y + 4 = 0, x^(2) + y^(2) - 2x - 4y + 1 = 0 and x^(2) + y^(2) + 2x - 8y + 1 = 0 are collinear. More over prove that their radii are in geometric pregression.

The circumcentre of the triangle made by the line segments joining the centres of the circles x^(2)+y^(2)-4=0;x^(2)+y^(2)-2x-4y+1=0 and x^(2)+y^(2)-6x-2y+6=0

The centres of 3 circles x^2+y^2 =1, x^2+y^2 +6x-2y=1, x^2+y^2-12x+4y=1 are :

Show that the centres of the following circles lie on a line and their radii are in A.P. : x^(2) + y^(2) = 1, x^(2) + y^(2) + 6x - 2y -6 = 0, x^(2) + y^(2) - 12x + 4y - 9 = 0 .

Find the centre and radius of the circle x^(2) + y^(2) - 6x + 4y - 12 =0 .