"Area of operation" means the area within the city or county activating an authority. Such term shall also mean any other city or county in which the authority wishes to operate, provided the governing authorities and the board of any hospital authorities of such city [...]

"Area of operation" may also mean the combined areas of operation of political subdivisions which participate in the creation of a common redevelopment agency to serve such participating political subdivisions as provided in subsection (d) of Code Section 3644436-44-4 [...]

"Area of operation" means the area within the corporate limits of the municipality or county and the area within five miles of such limits, except that it shall not include any area which lies within the territorial boundaries of another incorporated municipality or [...]

(1) "Area of operation" means the unincorporated area of the county in the case of counties and the territory located within the corporate limits of the municipality in the case of municipalities.