The Parabola

The parabola is something of a hybrid. it is a mathematical algebraic
concept (eg y = x^2) whose geometric properties make it interesting for
designing objects.

A circle can move in any direction and the inner relationships are always the
same until one introduces an orthogonal basis. Then we start dealing with sin and cos
functions. The directrix defining the parabola is an axis. The focus itself, then,
is the same distance from the vertex as the on the other side. The points of the parabola
will then be equidistant from the focus and the axis. Because the perpendiculars to the
directrix all reflect light toward the focus, the parabola is the best shape for
various instruments such as satellites and radars!!

see: Math is Fun Parabola

source: Wikipedia