Collar on the cone

Today I discovered that the loop I have been trying so hard to understand may in fact be a part of a cone!

The loop sits like a collar on the cone.

The loop photographed from the cone focal point.

This is a bit of a breakthrough! It's interesting that such a simple paper model can be so useful. In CAD, how would you constrain a straight strip to follow the shape of a (developable) cone?