In any case where an agency was activated in a community by a resolution adopted pursuant to Section 33101 prior to January 1, 1951, and where thereafter and prior to January 1, 1951, the legislative body of the community purported to dissolve the agency under circumstances where Section 33140 was not applicable, and where as a result of such purported dissolution the agency was inactive for a period of at least 10 years, and where subsequent to January 1, 1962, the legislative body of the community adopted an ordinance pursuant to Section 33101 declaring that there is need for an agency to function in the community, which ordinance was not suspended by referendum, and where subsequent to the adoption of such ordinance new members of the agency were appointed pursuant to Section 33110, such agency is a valid and existing agency with full power to transact any business and exercise its powers and the members appointed subsequent to the adoption of such ordinance are the legally appointed and existing members of the agency, each for the term designated in his appointment. For the purpose of applying Section 33140 to such agency, the two-year period referred to in that section shall be measured from the date of adoption of such ordinance.