Conic sections

A conic section is a curve formed when a plane cuts the curved surface of a right circular cone. The simplest such curve is the circle. The other conic sections are the ellipse, the parabola and the hyperbola.

How conic sections are formed

The following picture, borrowed from Wikipedia, shows nicely how conic sections are formed:

We start with an ordinary cone. We then cut the cone with a plane in different ways, and where the plane meets the cone it forms a new curve. We always consider only the curved surface of the cone, so we really do get just a curve – we ignore the inside of the cone.

Types of conic section

• An ellipse is a curve on which every point has the same sum of distances from two given points in the plane.
• A hyperbola is a conic section on which every point has the same absolute value of the difference of its distances from two fixed points.
• A parabola is a curve on which every point is the same distance from a given line and from a given point that does not lie on that line.