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By "double right cone" do you mean one right cone sitting normal with another right cone upside-down atop the first cone? If so, then we you take that double right cone and intersect it with a plane at different angles, you get the conic sections. (i.e. hyperbola, parabola, elipse, circle)

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If a right circular cone intersects a plane that runs parallel to the edge of the cone is what?

The intersection of a right circular cone and a plane that is parallel to the edge of the cone is a parabola. However, if the vertex of the cone lies on the plane, then the intersection is simply two intersecting lines.


What are conics?

Conics, or conic sections, are the intersection of a plane with an infinite double cone. If that plane cuts both cones, it is a hyperbola. If it is parallel to the edge of the cone, you get a parabola. If neither is the case, it is an ellipse. The ellipse is also a circle if the plane is perpendicular to the altitude of the cone. Note that none of these are the case if the plane passes through the vertex of the cone.


Right circular cone is intersected by a plane that is parallel to one edge of the cone?

I'm assuming you are looking for the name of the conic section produced by this type of intersection? If a right circular cone is intersected by a plane parallel to one edge of the cone, the resulting curve of intersection would be a parabola. If the intersecting plane was parallel to the base, it would be a circle. If the intersecting plane was at any angle between being parallel to the base and being parallel to an edge, it would produce an ellipse or part of an ellipse (depending on whether the intersection was completely within the cone).


What area is formed by a plane cutting through a solid perpendicular to its axis?

A cross section is formed.


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.

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