Hello, alexanderl33!;198760]

A plane intersects a double-napped cone and makes a 41° angle with the central axis.

The conic formed is an ellipse. The vertex angle of the cone must be less than . . .

Consider a cone with an 82° vertex angle.

The configuration looks like this. Code:

*
/|\
/ | \
/ | \
/41°|41°\ /
/ | \ /
/ | *
/ | / \
/ |41°/ \
/ | / \
/ | / \
/ |/ \
/ * \
/ / \

The intersecting plane is *parallel* to the slant of the cone.

The resulting conic curve would be a *parabola*.

For the plane to pass *through* the cone,

. . the vertex angle must be less than 82°.