The circle whose equation are x^2+y^2+c^2=2ax and x^2+y^2+c^2=2by will touch one another externally,if

Center is same so both the circles can`t touch externally if they are touchimg then they touch infernally

Here the center are not same of two circle so they can`t touch internally they touch externally but I want this condition what. Is the condition for this

Sorry there is mistake in my answer, we can write circle equation as (x-a)^2 + y^2 = a^2-c^2 so by this center is (a,0) and radius is √(a^2-c^2) similarly for Nother circle the equation as x^2+(y-b)^2 = b^2-c^2 so the center is (0,b) and radius is √(b^2-c^2) ao if two circles are touching externally then the realtion between them is C1C2=r1+r2 means distance between center = sum of radii of both the circles so by this √(a^2+b^2)=√(a^2-c^2) + √(b^2-c^2) so further if u solve this u will found out that c^2(a^2+b^2)=a^2.b^2 and it equals to 1/c^2= 1/a^2 + 1/b^2.

Approved