(a) All airport zoning regulations adopted under this chapter shall provide for an administrative agency to have and exercise the following powers:

(1) To hear and decide any special exceptions to the terms of the airport zoning regulations upon which such agency may be required to pass under such regulations.

(2) To authorize in specific cases such variance from the terms of the ordinance as will not be contrary to the public interest, where, owing to special conditions, a literal enforcement of the provisions of the ordinance will result in unnecessary hardship, and so that the spirit of the ordinance shall be observed and substantial justice done.

(b) The agency shall not be required to return the original papers acted upon by it, but it shall be sufficient to return certified or sworn copies thereof or of such portions thereof as may be called on by such writ. The return shall concisely set forth such other facts as may be pertinent and material to show the grounds of the decision appealed from and shall be verified.

(c) The agency shall adopt rules in accordance with the provisions of the ordinance or resolution by which it was created. Meetings of the agency shall be held at the call of the chairman and at such other times as the agency may determine. The chairman, or in his absence the acting chairman, may administer oaths and compel the attendance of witnesses. All hearings of the agency shall be public. The agency shall keep minutes of its proceedings, showing the vote of each member upon each question, or, if absent or failing to vote, indicating such fact, and shall keep records of its examinations and other official actions, all of which shall immediately be filed in the office of the agency and shall be a public record.