The parabola is special type of curve that has a focal point to which parallel beams of light will be reflected. The opposite is also true, a light source placed at the focus will create a parallel beam of light, as in a spotlight.
A parabola is the shape of the path of a projectile fired into the air and allowed to fall again (assuming no friction from the air), or a stone that is thrown into the air.
It is also the shape obtained if you were to cut a cone shape along a line parallel to it's side.
The shape is not part of a circle or an ellipse, and all parabolas are the same shape, they only differ in their size and the portion of the shape that you use. In other words you do not get pointed parabolas and blunt or flat ones. A parabola that appears to be just a shallow dish, is the same shape as the very top part of the path traced by a stone thrown in the air.
Parabolic reflectors are used in one of two ways:
The Parabolic Trough
A 2 dimensional parabola which you will see when looking on the end of the trough. In this arrangement, light will be focussed onto a line that runs the entire length of the trough. Normally a tube will run the length of the trough at the focal point carrying a liquid that will be heated the sun's energy.
To maintain the focus of sunlight on the tube, a tracking mechanism will be necessary to change the vertical angle of the trough as the sun rises and falls in the sky.
The Parabolic Dish
This is in effect a 3 dimensional parabola, you will be able to see the parabolic shape looking from any side. These reflectors will focus light onto one point and are typically used to provide the energy for Stirling Engines running generators.
To maintain the focus of light on the Stirling Engine, a tracking system will need to follow the movement of the sun vertically and horizontally.