ConicSection

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 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 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

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