Edit made on November 17, 2008 by derekcouzens at 20:11:06
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A conic section is the curve obtained by the intersection of a plane and a cone (a conic surface).
* 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