Hollow core doors are light weight, but are easy to damage. Door hinges can become loose in hollow core doors fairly easily. Remember, a hollow core door has solid wood only around the perimeter of the door and at the handle area.
If you have a loose hinge, obviously try tightening it slightly with a screwdriver. You may be done at this point. If the screw just turns and doesn’t tighten the hinge, the hole is probably reamed out and there isn’t enough wood for the screw threads to bite into. For this you can try a larger screw with more aggressive threads. If this fails, fill in the hole with a golf tee and use adhesive to glue it in place. Once it has dried, you can pre-drill a hole and reinstall the original screw (if it is in good shape). You may have to do this at more than one screw location.
If the hinge is loose at the jamb, you have more options. Certainly you can use the golf tee trick, but you can also use a longer screw. A longer screw at the jamb will eventually reach the framing behind the jamb, whereas where the hinge meets the door, there is only empty space with a cardboard-like material because it is hollow.
