The following regulations shall govern the granting of variances:
(a) Where the City Planning Commission finds that extraordinary and unnecessary hardship may result from strict compliance with these Regulations due to exceptional topographic or other physical conditions, it may vary the regulation so as to relieve such hardship, provided such relief may be granted without detriment to the public interest and without impairing the intent and purpose of these Regulations, or the desirable development of the neighborhood and co unity. Such variations shall not have the effect of nullifying the intent and purpose of this chapter, the master plan or the Zoning Code.
(b) In granting the variances or modifications, the City Planning Commission may require such conditions as will, in its judgment, secure substantially the objective of the standards of requirements so varied or modified.