Answer:
based on a false belief
Explanation:
Word illusive means that something is deceiving, misleading, showing that which does not exists. It is used for illusions or things that do not actually exist, but some might claim that they do.
This is the way it is used for her. It refers to the false belief in the existence of the fountain of youth. The fountain obviously does not exist, yet people falsely think it does, they go to search for it and follow the illusion of the idea.
