The other day, I was reading up on the synthetic geometry of conic sections a bit, and I wondered: is it possible to construct the hyperbola's asymptotes given just the intersecting plane and the Dandelin spheres? Are the asymptotes and the Dandelin spheres connected in any non-trivial/interesting way? I know there's a fairly obvious connection between the spheres and the hyperbola's foci and directrices.
Thanks!