The circles whose equations are x2+y2+c2=2ax and x2+y2+c2−2by=0 will touch one another externally, if

The two circles arex2+y2−2ax+c2=0 and x2+y2−2by+c2=0Centres and radii of these two circles areCentres C1(a,0)C2(0,b)r1=a2−c2r2=b2−c2Radii: Given that the two circles touch each other externally. ∴ C1C2=r1+r2⇒ a2+b2=a2−c2+b2−c2⇒ a2+b2=a2−c2+b2−c2+2a2−c2b2−c2⇒ c4=a2b2−c2a2+b2+c4⇒ a2b2=c2a2+b2⇒1a2+1b2=1c2