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.

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Originally Posted by ebaines

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.

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

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Originally Posted by nykkyo

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

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Yes, that would do it.