# What is a parabola?

Andrey Kim

February 5, 2015

Parabola - the curve of the second order, corresponding in the rectangular coordinate system to the equation y2= 2px. Let's take a closer look at what a parabola is and give its rigorous mathematical definition.

## Parabola scientifically

The study of a parabola is included in the school course of geometry, many people remember the appearance of this curve, but few can reproduce its scientific definition. Here’s how it sounds: a parabola is a geometric locus of points that are equidistant from a certain point (focus) and a certain straight line (director).

## Parabola properties

- The axis of symmetry of a parabola is a straight line drawn from its focus and perpendicular to the director.
- The optical property is the most remarkable property of a parabola. If the source of light is placed at the focus of the parabola, then the rays of the source will create a parallel beam when reflected from the parabola. This feature is used in the construction of parabolic antennas.
- All parabolas are similar, the distance between the focus and the directrix determine the scale of the parabola.