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A conic section is the curve obtained by the intersection of a plane and a cone (a conic surface).

These are:

* circle - cutting perpendicular to the centre line

* ellipse - cutting at an angle between the centre line and the slope angle.

* parabola - cutting parallel to one edge

* hyperbola - cutting parallel to the centre line

* circle - cutting perpendicular to the axis of symmetry of the cone

* ellipse - cutting at an angle less than the slope angle.

* parabola - cutting at an angle equal to the slope angle

* hyperbola - cutting at an angle greater than the slope angle

| http://upload.wikimedia.org/wikipedia/commons/9/97/Conic_section_(PSF).png |

| |>> Image courtesy of the wiki commons. <<| |

There are some degenerate cases:

* point - a degenerate circle

There are some degenerate cases i.e. when the cutting plane passes through the apex of the cone:

* point - a degenerate circle (or ellipse)

* line - a degenerate parabola

* intersecting lines - a degenerate hyperbola