Conic Sections

 Conic Section :

Circle

Each of these figures (Circle, ellipse, hyperbola and parabola) are created by intersecting cones that are stacked on top of each other (double cones) with a plane (the flat paper-like thing shown in the pictures).  Thus, the figures are called conic sections or conics. If the plane cuts completely across one cone and is perpendicular to the axis of the cone, the curve of the section is called a circle.

Ellipse

If the plane isn't perpendicular to the axis of the cone (if it is slanted), it is called an ellipse.

Parabola

If the plane doesn't cut across one entire cone or intersect both cones, the curve of the intersection is called a parabola.

A parabola is the set of all points in a plane equidistant from a fixed point and a fixed line in the plane.

Hyperbola

If the plane cuts through both nappes of the cone, the curve is called a hyperbola.

The hyperbola is the set of all points in a plane. The difference of whose distance from two fixed points in the plane is the positive constant.

Here is a great link that directs you to a webpage that gives in-depth, yet easy to understand information on conic sections and their equations. http://www.mathacademy.com/pr/prime/articles/conics/index.asp