On points constructible from conics (Q1361177)

It is known that some geometric constructions are impossible if one uses just a straightedge and compass. What if one is allowed to use conics? It was known to the ancient Greeks that (i) duplication of the cube is possible by using a parabola (Menaechmus), (ii) trisection of an arbitrary angle is possible by using a hyperbola (Pappus), (iii) a regular heptagon can be constructed (Archimedes). In the present paper, the author considers the problem of which points are constructible from conics. In particular, he determines which regular polygons are conic-constructible.