DEFINITION
parabola
A parabola is the set of points in a plane that are the same distance from a fixed point
(called the focus), and a fixed line (called the directrix).
To explore this definition, investigate the diagram at right.
Pick any point on the parabola (say, $\,\text{P}1\,$).
Pick a different point on the parabola (say, $\,\text{P}2\,$).
No matter what point you choose on a parabola,
You can play with parabolas here. 

Parabolas have some beautiful geometric properties
REFLECTING PROPERTY OF PARABOLAS
Rays emanating from the focus will always be reflected perpendicular to the directrix.
To explore this property, investigate the diagram at right.
Place a light at the focus. This ability of parabolas to generate straight, focused beams of light makes them valuable in applications as varied as laser surgery and the Hollywood beams of light! This same geometric property also allows parabolas to act as collectors:
COLLECTING PROPERTY OF PARABOLAS
Rays entering the parabola perpendicular to the directrix are always reflected so that they
pass through the focus.
Think about the satellite dish on the outside of a house. Beams enter the dish at all possible angles, but those that come in perpendicular to the directrix are all focused on a single point, where a device collects the signal, amplifies it, and sends it into the house. Thus, the name focus is appropriate for this special point! 

VERTEX OF A PARABOLA
The vertex of a parabola is the point that is exactly halfway between the focus and the directrix.
It is the point where the parabola turns (i.e., changes direction). 

The distance between the focus and the vertex affects the shape of the parabola, as shown below.
As the focus moves farther away from the vertex, the parabola gets wider (flatter).
In any orientation of a parabola, the focus is always inside the parabola. 

