CAD tip # 8322:

This can be done with the XEDGES command, where you just select a 3D solid (3DSOLID), 3D mesh (3DMESH) or 3D surface (SURFACE) object. Its edges (wires, wireframe) are extracted as new simple entities in 3D - lines, arcs or splines (as neccessary - from the geometry shape).

If you want to get the 3D intersection curve of two separate 3D solids (e.g. a conic section), first convert these solids to a single body - e.g. with the UNION command.

If you want to extract only a selected edge, use the command OFFSETEDGE with the option Distance = 0.