Show that the circle passing through the origin and cutting the circles `x^2+y^2-2a_1x-2b_1y+c_1=0` and `x^2+y^2-2a_2x -2b_2y+c_2=0` orthogonally is `|(x^2+y^2,x,y),(c_1,a_1,b_1),(c_2,a_2,b_2)|=0`

Find the equation of circle passing through the origin and cutting the circles x^(2) + y^(2) -4x + 6y + 10 =0 and x^(2) + y^(2) + 12y + 6 =0 orthogonally.

The locus of the centre of the circle passing through the intersection of the circles x^2+y^2= 1 and x^2 + y^2-2x+y=0 is

The equation of the circle which pass through the origin and cuts orthogonally each of the circles x^2+y^2-6x+8=0 and x^2+y^2-2x-2y=7 is

The locus of the centre of the circle cutting the circles x^2+y^2–2x-6y+1=0, x^2 + y^2 - 4x - 10y + 5 = 0 orthogonally is

The locus of the centres of circles passing through the origin and intersecting the fixed circle x^(2)+y^(2)-5x+3y-1=0 orthogonally is

Prove that the general equation of circles cutting the circles x^2 + y^2 + 2g_r x + 2f_r y+c_r = 0, r= 1, 2 orthogonally is : |(x^2+y^2,-x,-y),(c_1,g_1,f_1),(c_2,g_2,f_2)|+k|(-x, -y, 1), (g_1, f_1, 1), (g_2, f_2, 1)| =0

The radius of the circle passing through the points of intersection of ellipse x^2/a^2+y^2/b^2=1 and x^2-y^2 = 0 is

Show that the circles x^(2)+y^(2)-6x+4y+4=0and x^(2)+y^(2)+x+4y+1=0 cut orthogonally.

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

If two circles x^(2)+y^(2)+2a_(1)x+2b_(1)y=0 and x^(2)+y^(2)+2a_(2)x+2b_(2)y=0 touches then show that a_(1)b_(2)=a_(2)b_(1)