We　first　prove　that　the　subcategory　of　fixed　points　of　mutation　determined　by　an　exceptional　object　E　in　a　triangulated　category　coincide　with　the　perpendicular　category　of　E.　Based　on　this　characterisation,　we　prove　that　the　subcategory　of　fixed　points　of　mutation　in　the　derived　category　of　the　coherent　sheaves　on　weighted　projective　line　with　genus　one　is　equivalent　to　the　derived　category　of　a　hereditary　algebra.　Meanwhile,　we　induce　two　new　recollements　by　left　and　right　mutations　from　a　given　recollement.