The point of reflection of (m,n) on the line y−x=0 is (n,m), so equation of circle having centre (n,m) and let radius r is (x−n)2+(y−m)2=r2.....(i) ∵ Circle (i) touches the X− axis, so r=m So, equation of required circle is (x−n)2+(y−m)2=m2 or x2+y2−2nx−2my+n2=0