Changes

[[image:Conic sections.gif|right|A two dimensional representation of the four major conic sections]]

[[image:Conic sections.gif|right|A two dimensional representation of the four major conic sections]]

A [[conic section]] is the two dimensional curve that is the intersection of a plane with a right circular [[cone]].  In mathematics, a cone extends to infinity, and goes in both directions from its apex.

A '''conic section''' is the two dimensional curve that is the intersection of a plane with a right circular [[cone]].  In mathematics, a cone extends to infinity, and goes in both directions from its apex.

Depending on the orientation of the plane relative to the cone, the conic section produced will be:

Depending on the orientation of the plane relative to the cone, the conic section produced will be:

*A [[hyperbola]], if the plane is at an angle to the axis smaller than the cone's apex.  Most hyperbolas are thus two separate curves, resulting from the plane intersecting both "halves" of the cone.

*A [[hyperbola]], if the plane is at an angle to the axis smaller than the cone's apex.  Most hyperbolas are thus two separate curves, resulting from the plane intersecting both "halves" of the cone.

'''Special cases'''

'''Degenerate conics'''

*If the plane is tangent to the cone, a line is produced

*If the plane is tangent to the cone, a line is produced

*If the plane intersects the apex of the cone only, the result is a point.

*If the plane intersects the apex of the cone only, the result is a point.

[[category:mathematics]]

[[Category:Mathematics]]