Conic sections

A conic section is the curve formed by the intersection of a plane and a double-napped right circular cone. The type of curve depends on the angle and position of the plane relative to the cone's axis.

Important properties

• There are four main types: circle, ellipse, parabola, and hyperbola.

• Each conic section has a standard equation in the coordinate plane.

• Conic sections can also be defined using distances from points (foci) and lines (directrix).

• The eccentricity ($e$) distinguishes the types: $e=0$ (circle), $0<e<1$ (ellipse), $e=1$ (parabola), $e>1$ (hyperbola).