Well you know I was looking at my lamp one day (the og 25s might remember this) and you know you the light that comes the light bulb radially produces a sphere? Well the lamp shade cuts it off in circles, so you’re left with a “sector” of a sphere, ie a cone. This cone of light intersects the walls, casting a particular shape on it.
Recall conic sections:
View attachment 48721
the wall is vertical, and as such makes a vertical cut to the cone of light, casting a HYPERBOLA on the wall
View attachment 48722
proof by exhaustion on desmos
so everytime you use a torch or lamp or other conic light source you’re casting hyperbolas, parabolas, ellipses and circles