Let the variable circle is x2+y2+2gx+2fy+c=0.....(1) It passes through (a,b) ∴a2+b2+2ga+2fb+c=0 (1) cuts x2+y2=4 orthogonally ∴2(g×0+f×0)=c−4⇒c=4 ∴ from (2) a2+b2+2ga+2fb+4=0 ∴ Locus of center (−g,−f) is a2+b2−2ax−2by+4=0 or 2ax+2by=a2+b2+4