Conical Sections

Conical Sections

1. A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic sections are the hyperbola, the parabola, and the ellipse. The circle is type of ellipse, and is sometimes considered to be a fourth type of conic section.

   • A hyperbola is the set of all points where the difference between their distances from two fixed points (the foci) is constant. In the case of a hyperbola, there are two foci and two directrices. Hyperbolas also have two asymptotes.
   • A parabola is the set of all points whose distance from a fixed point, called the focus, is equal to the distance from a fixed line, called the directrix. The point halfway between the focus and the directrix is called the vertex of the parabola.
   • An ellipse is the set of all points for which the sum of the distances from two fixed points (the foci) is constant. In the case of an ellipse, there are two foci, and two directrices.