PARABOLA

Definition of a Parabola

The parabola is defined as the locus of a point which moves so that it is always the same distance from a fixed point (called the focus) and a given line (called the directrix).

In the following graph,

• The focus of the parabola is at (0,p).
• The directrix is the line y=−p.
• The focal distance is |p| (Distance from the origin to the focus, and from the origin to the directrix. We take absolute value because distance is positive.)
• The point (x, y) represents any point on the curve.
• The distance d from any point (x, y) to the focus (0,p) is the same as the distance from (x, y) to the directrix.

 

The parabola has many APPLICATIONS in situations where:

• Radiation often needs to be concentrated at one point or radiation needs to be transmitted from a single point into a wide parallel beam (e.g. headlight reflectors).

Here is an animation showing how parallel radio waves are collected by a parabolic antenna. The parallel rays reflect off the antenna and meet at a point (the red dot, labelled F), called the focus.