Move the dots, press Space to draw the conic, and press x to clear and stop drawing.
Yoinked a line intersection finder from rubiks_cube_guy238 because I couldn't be bothered. Otherwise, the general idea is that the program uses pascals theorem to find the particular conic that is described by 5 points. Works well, and is near instant in turbo mode, sometimes has a dot at the origin, probably from a div/0 error somewhere.
