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Conic sections

Conic sections · Diagrams

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Four plane cuts of a double cone

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Four 3D schematics: a plane parallel to the base gives a circle; a tilted plane through one nappe gives an ellipse; a plane parallel to a generator gives a parabola; a vertical plane through both nappes gives two hyperbola branches. Blue marks each intersection and orange its cutting plane. The finite cones truncate open curves; circles appear foreshortened in the 3D projection.
Four 3D schematics: a plane parallel to the base gives a circle; a tilted plane through one nappe gives an ellipse; a plane parallel to a generator gives a parabola; a vertical plane through both nappes gives two hyperbola branches. Blue marks each intersection and orange its cutting plane. The finite cones truncate open curves; circles appear foreshortened in the 3D projection.
Four 3D schematics: a plane parallel to the base gives a circle; a tilted plane through one nappe gives an ellipse; a plane parallel to a generator gives a parabola; a vertical plane through both nappes gives two hyperbola branches. Blue marks each intersection and orange its cutting plane. The finite cones truncate open curves; circles appear foreshortened in the 3D projection.
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