Let the equation of circle be, x2+y2+2gx+2fy+c=0 The circle passes through the point (1,0) Hence, 1+2g+c=0 The circle is cutting the circles x2+y2−2x+4y+1=0 and, x2+y2+6x−2y+1=0 orthogonally. So, 2g(−1)+2f(2)=c+1 And, 2g(3)+2f(−1)=c+1 Therefore, f=0 g=0 And, c=−1 Hence, the equation of required circle is x2+y2=1 and its centre is (0,0)