If one of the circles `x^2+y^2+2ax+c=0` and `x^2+y^2+2bx+c=0` lies within the other, then

If the circles x ^2 + y ^2 + 2ax + c = 0 and x ^2 + y ^2 +2by + c = 0 touch each other, prove that 1/a ^2 + 1 b ^2 = 1/c

Show that the circles x^2 +y^2 + 2ax + c = 0 and x^2 + y^2 + 2by + c = 0 touch each other if 1//a^2 + 1//b^2 = 1//c.

If the circles x^2 + y^2 + 2ax + b = 0 and x^2+ y^2+ 2cx + b = 0 touch each other (a!=c)

If the circles x^2+y^2+2ax+c=0 and x^2+y^2+2by+c=0 touch each other, then find the relation between a, b and c .

Show that the circles x^(2) +y^(2) + 2ax + c=0 and x ^(2) + y^(2) + 2by + c=0 to touch each other if (1)/(a^(2)) + (1)/( b^(2)) = (1)/( c )

If the circles x^(2)+y^(2)+2ax+c=0 and x^(2)+y^(2)+2by+c=0 touch each other,then find the relation between a,b and c.

If the circles x^2+y^2+2ax+c=0 and x^2+y^2+2by+c=0 touch each other , prove that c is always positive .

If two circles and a(x^2 +y^2)+bx + cy =0 and p(x^2+y^2)+qx+ry= 0 touch each other, then