Any improvement district created under RCW 35.43.200- 35.43.230 shall be created only by ordinance defining its boundaries as specified and described in the petition therefor and specifying the plan or system therein provided for; and shall be initiated only upon a petition therefor, specifying and describing the boundaries of such district and specifying the plan or system of proposed improvement, signed by the owners of at least sixty percent of the lineal frontage upon the proposed improvement and of at least fifty percent of the area within the limits of the proposed improvement district: PROVIDED, That the city council may in its discretion reject any such petition.