If two circles `x^(2)+y^(2)+c^(2)=2ax` and `x^(2)+y^(2)+c^(2)-2by=0` touch each other externally , then prove that `(1)/(a^(2))+(1)/(b^(2))=(1)/(c^(2))`

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

If circles (x -1)^(2) + y^(2) = a^(2) " and " (x + 2)^(2) + y^(2) = b^(2) touch each other externally , then

If two circles x^(2) + y^(2) - 2ax + c = =0 and x^(2) + y^(2) - 2by + c = 0 touch each other , then c =

If the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2) touch each other, then

If the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2) touch each other, then

The circles x^(2)+y^(2)+2x-2y+1=0 and x^(2)+y^(2)-2x-2y+1=0 touch each other

The circles x^(2)+y^(2)+2x-2y+1=0 and x^(2)+y^(2)-2x-2y+1=0 touch each other