Cylinder/Plane intersection

[markraz]

If a cylinder intersects a plane and they are not perpendicular, does the resulting intersection on the plane always form an an ellipse?

thanks

 

[pka]

If a cylinder intersects a plane and they are not perpendicular, does the resulting intersection on the plane always form an an ellipse?

The statement of your question is problematic. If this is a right circular cylinder then the intersection could one line or two parallel lines if the normal of the plane is perpendicular to the central axis of the cylinder. If the normal of the plane is not perpendicular nor parallel to the central axis of the cylinder then the intersection is an ellipse.

 

[markraz]

The statement of your question is problematic. If this is a right circular cylinder then the intersection could one line or two parallel lines if the normal of the plane is perpendicular to the central axis of the cylinder. If the normal of the plane is not perpendicular nor parallel to the central axis of the cylinder then the intersection is an ellipse.

oops yeah I didn't think of that, thanks, So basically there are 3 scenarios? and green would always be an ellipse?
so as long as it is not perpendicular or parallel on the plane it is an ellipse?
thanks