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When a cone is sliced parallel to the base then the shape produced is a circle.
If the cone is sliced at an angle so that the cut goes completely through the cone then an ellipse is produced.
If the cut is made perpendicular to the cone's base then the shape produced is a parabola.
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BlakeThe following plane figures are obtained when a right circular cone is sliced by a plane.
If the slicing plane is parallel to the base of the cone you will get a circle.If the slicing plane is inclined to the base of the cone at an angle that is smaller than the incline of the cone, you will get an ellipse.
If the slicing plane is inclined to the base of the cone at an angle that is the same as the incline of the cone, you will get a parabola.
If the slicing plane is inclined to the base of the cone at an angle that is greater than the incline of the cone, you will get half a hyperbola.
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If a right circular cone is intersected by a plane that passes through only one nappe of the cone but is not parallel to an edge of the cone what shape is produced?
An ellipse is produced.
A plane figure formed by the intersection of a double right cone and a plane?
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)
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.
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).
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.
