"Conic " sections on hyperboloid

Question

What are eccentricities of "Conic" section created by intersection of a one sheet hyperboloid ( meridian $e >1 $) with a plane at inclination $\phi?$

Which inclination results in a hyperbola? a parabola? Thanks in advance.

Answer 1

I don't have the answers but I think you can find them in the book New Horizons in Geometry by Tom M. Apostol and Mamikon A. Mnatsakanian, 2012.

or here

New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors (same authors as above) https://www.tandfonline.com/doi/abs/10.1080/00029890.2008.11920594