The Board of Zoning Appeals shall hear and decide appeals made for exceptions to and variations from the application of ordinances, orders, and regulations of City administrative officials or agencies, governing building and zoning in the City. Such appeals and decisions shall be in conformity with the purpose and intent of such ordinances and regulations. The Zoning Board of Appeals shall have such other duties as Council may designate that are not inconsistent with the powers and duties provided for in this section.