Let the center be (α,β) As It cuts the circle x2+y2=p2 orthogonally ∴ Using 2g1g2+2f1f2=c1+c2, we get 2(−α)×0+2(−β)×0 =c1−p2⇒c1=p2 Let equation of circle is x2+y2−2αx−2βy+p2=0 It passes through (a,b)⇒a2+b2−2αa−2βb+p2=0 ∴ Locus of (α,β) is ∴2ax+2by−(a2+b2+p2)=0