The equation of normals is expressed as, x2−3xy−3x+9y=0 (x−3y)(x−3)=0 If, x=3 then, y=1 Thus, the coordinate of centre is (3,1) . The equation of the circle is, x2+y2−6x+6y+17=0 The radius of circle is calculated as, r1=√32+(−3)2−17 =1 The distance between the centers is calculated as, r1+r2=√(3−3)2+(1−(−3))2 r2=3 The required equation of the circle is expressed as, x2−6x+9+y2−2y+1=9 x2+y2−6x−2y+1=0