If the circle `x^(2)+y^(2)+2gx2fy+c=0` bisects the circumference of the circle `x^(2)+y^(2)+2g'x+2f'y+c'=0`, then prove that `2g'(g-g')+2f'(f-f')=c-c'`.

If the circle x^(2) + y^(2) + 4x + 2y + c = 0 bisects the cirucumference of the cirlce x^(2) + y^(2) -2x -8y -d = 0 then c + d =

If the circle x^(2) +y^(2) + 2gx + 2fy + c = 0 bisects the circumference of the circle x^(2) +y^(2) + 2g'x + 2f'y + c' = 0 , them the length of the common chord of these two circles is

If the circle x^2+y^2 +4x+22y + c = 0 bisects the circumference of the circle x^2 + y^2-2x + 8y-d = 0 ,then (c+d) is equal to

If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the circle x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0 then prove that 2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '

If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the circle x^2+y^2+2g^(prime)x+2f^(prime)y+c^(prime)=0 then prove that 2g^(prime)(g-g^(prime))+2f^(prime)(f-f^(prime))=c-c '

Show that the condition that the circle x^2+y^2+2g_1x+2f_1y+c_1=0 bisects the circumference of the circle x^2+y^2+2g_2x+2f_2y+c_2=0 is 2(g_1-g_2)g_2+2(f_1-f_2)f_2=c_1-c_2

The circle x^(2) + y^(2) + 2g x + 2fy + c = 0 does not intersect the y-axis if

If the point (2,-3) lies on the circle x^(2) + y^(2) + 2 g x + 2fy + c = 0 which is concentric with the circle x^(2) + y^(2) + 6x + 8y - 25 = 0 , then the value of c is

The line ax+by+by+c=0 is normal to the circle x^(2)+y^(2)+2gx+2fy+d=0, if

If theline y=x touches the circle x^(2)+y^(2)+2gx+2fy+c=0 at P where OP=6sqrt2 then c=