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A conic section is the intersection of a plane and a cone.

The circle is a conic section where the plane is perpendicular to the axis of the cone. The special case of a point is where the vertex of the cone lies on the plane.

The ellipse is a conic section where the plane is not perpendicular to the axis, but its angle is less than one of the nappes. The special case of a point is where the vertex of the cone lies on the plane.

The parabola is a conic section where the plane is parallel to one of the nappes. The special case of two intersecting lines is where the vertex of the cone lies on the plane.

The hyperbole is a conic section where the angle of the plane is greater than on of the nappes. There are two sides to the hyperbole. The special case of two lines intersecting is where the vertex of the cone lies on the plane.

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