I ran into this problem in a textbook and was intrigued by it. Conics are generally formed through different cuts one can make with the shape of a cone. But, there have been recent discussions on creating conical shapes through aiming a flashlight in a certain direction, which is interesting.
If you hold a flashlight parallel to the ground, the beam would be able to create a parabolic shape on the ground, which is one of the three conical shapes that can be made through a flashlight. Similarly, if one tilts a flashlight by aiming it on the wall, it could create an elliptical shape. However, I'm uncertain about what one can do to create a hyperbolic shape with a flashlight.
This picture is the reference for this problem and asks two things which I'm wondering if anyone has input on: (a) Why is the boundary of this lighted area a hyperbola? (b) How can one hold a flashlight so that its beam forms a hyperbola on the ground?