With my recently bought LED stab lamp the following "experiment" was done. Put the lamp on a table and watched the circle on the ceiling of the room. Then I positioned myself in the room in a certain distance and saw then the ellipse on the ceiling. Took a photo by the way. The question I am unable to calculate: what is the formula for the ellipse that one sees. It reminds me to a brochure of HP where maybe a similar problem was solved in the "computer graphics" formulas. Both pure 3D but maybe also 4D matrix calculations (?) are welcome. Of course any "elementary" of solving.
Addendum 20171003:
Want to direct your attention to two texts of David Eberly dealing with a maybe more than similar problem and delivering the math that might be helpful when occupying oneself with the above question. The titles are
David Eberly-Parallel Projection of an Ellipse
David Eberly-Perspective Projection of an Ellipse 20150310
You may visit the homepage of Dave.
Just a hint, maybe of some use.
The point source emits a cone of light, and the intersection with a plane perpendicular to the cone axis is indeed a circumference.
Imagine you are just above the spot, you somehow manage (transparent ceiling?) to observe it straight below your head, with our eyes at $A$ in the sketch below: you will see a circumference, the blod black line representing a diameter of it.
Now you start moving along a direction of your choice without varying your distance from the ceiling.
The sketch above is taken on a plane perpendicular to the ceiling, and containing the line along which you are moving. The bold black line represents the side view of the circle. The perceived size of one axis is related to the angle subtended by the bold black line and your eyes.
Of course another such angle can be characterised, subtended by your eyes and the diameter of the circumference that goes through the middle of the black line, perpendicular to the plane used for the sketch.
The two subtended angles define the perceived ellipse.