How can a circular conic section belong to thr same plane as an elliptical conic section?

Hint: note that a circle is the special case of an ellipse with equal length major and minor axis. So you can cut the cone with a plane perpendicular to the axis to get a circle, and also say the result is an ellipse.

Hint: note that a circle is the special case of an ellipse with equal length major and minor axis. So you can cut the cone with a plane perpendicular to the axis to get a circle, and also say the result is an ellipse.
I think for this to happen the comon plane must cut two rotated cones

I think for this to happen the comon plane must cut two rotated cones

Yes, that would do it.