An active location is part of the quest. But a quest is not part of the active location. Per the rules:
Instead, an active location acts as a buffer for the
currently revealed quest card. Any progress tokens
that would be placed on a quest card are instead placed
on the active location. If a location ever has as many
progress tokens as it has quest points, that location is
considered explored and is discarded from play.
To Dam, BitJam listed the two cards in the core game that place on the Quest (instead of specifying just a location): Legolas and Blade of Gondolin.