"Tatăl ei este regizor."
Translation:Her father is a director.
So "her father is director" was correct and in English this is the same as saying "the director" implying both speaker and listener know which director is the subject. I suspect "a director" would have been accepted here as well but takea on a different meaning. Is there a difference in Romanian?
Un regizor - a director / Regizorul - the director
"Regizorul" implies you know what director are you talking about, "un regizor" does not.