The centres of the three circles `x^2 + y^2 - 10x + 9 = 0, x² + y^2 - 6x + 2y + 1 = 0, x^2 + y^2 - 9x - 4y +2=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.

Prove that the centres of the three circles x^2 + y^2 - 4x – 6y – 12 = 0,x^2+y^2 + 2x + 4y -5 = 0 and x^2 + y^2 - 10x – 16y +7 = 0 are collinear.

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.

The centres of the three circles x^(2)+y^(2)-10x+9=0,x^(2)+y^(2)-6x+2y+1=0,x^(2)+y^(2)-9x-4y+2=0

The centres of the three circles x^(2)+y^(2)-10x+9=0, x^(2)+y^(2)-6x+2y+1=0, x^(2)+y^(2)-9x-4y+2=0 lie on the line

Prove that the centres of the three circles : x^2 + y^2 -4x-6y-14=0, x^2 + y^2+ 2x+4y-5=0 and x^2 + y^2-10x -16y + 7 = 0 are collinear.

The equation of the circle which cuts orthogonally the three circles x^(2) + y^(2) + 4x + 2y + 1 = 0 , 2x^(2) + 2y^(2) + 8x + 6y - 3 = 0 , x^(2) + y^(2) + 6x - 2y - 3 = 0 is

The locus of the centre of the circle which cuts the circles x^(2) + y^(2) + 4x - 6y + 9 = 0 " and " x^(2) + y^(2) - 5x + 4y + 2 = 0 orthogonally is