“Area of operation” means either of the following:
(a) In the case of an authority created by a city, the area within its boundaries. It does not include any area which lies within another city unless the governing body of the other city has consented by resolution or ordinance. It does not include any area which lies within the unincorporated area of any county.
(b) In the case of an authority created by a county, all of the county except the area within any city.