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If a right circular cone is intersected by a plane so that the intersection goes through the cone's vertex as well as an edge of each nappe, the shape produced is a line.

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If the angle of the plane is less than the angle of the cone, then the intersection is a point. If the angle of the plane is greater than the angle of the cone, then the intersection is two lines intersecting at the vertex.

If the plane insersects at other than the vertex, then the intersection is a circle when the plane is perpendicular to the cone's axis, an ellipse when the plane's angle is less than the cone's angle, a parabola when the planes's angle equals the cone's angle, and two hyperbole's in the last case.

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Q: If a right circular cone is intersected by a plane so that the intersection goes through the cone's vertex as well as an edge of each nappe what shape is produced?
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Related questions

If a circular cone is intersected by a plane so that the intersection goes through its vertex as well as the edge of the nappe what shape is produced?

If I understand your description correctly, a line.


If a right circular cone is intersected by a plane that goes through both nappes of the cone but not through the vertex as in the picture below what shape is produced?

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