The most extensive antique study regarding conic sections comes to us from Apollonius of Perga (III-II centuries B. C.). Among other things, Apollonius demonstrates a series of properties which lead to important applications in the fields of Science and Technology.

In the ellipse there are two points, called focuses, placed on the longer diameter so that the sum of the distances of any point of the curve from the focuses is the same. This factor can be used to trace an ellipse which is very approximate, but accurate enough to make, for example, elliptic flowerbeds (in fact it is known as the gardener ellipse).

A second property of the focuses of an ellipse consists in the fact that the perpendicular to the ellipse in any point divides the angle formed by the segments joining this point to the two focuses in half. Consequently, a ray of light originating from one of the focuses, and reflected on the ellipse, passes through the other focus.

The same happens with sound waves. If one speaks standing in one of the focuses of an elliptic vault room, the sound waves will be reflected by the vault and will gather in the other focus.

In the circle both focuses are in the centre. As the ellipse gets longer the focuses get further apart. The parabola has only one focus, the other one has (so to speak) gone to infinity. The rays that come from this focus and go to infinity are parallel lines. Reflecting on the parabola these rays will gather in the remaining focus.

Therefore, if we want to gather some parallel lines (or practically parallel, like sun rays, for example) in a certain point, we'll need to use a glass with the shape of a parabola. In so doing it is possible to construct a burning glass, capable of burning a piece of paper or wood put in its focus. The legend - for that is how it should be considered - according to which Archimedes (III century B.C.) burnt Roman ships with a burning mirror gave rise to a considerable amount of reseach in this direction until the late 17th century.

The big radio telescopes and parabolic antennas used to receive television transmissions from satellites, work according to the same principle. The practically parallel signals (considering the great distance they come from), reverberate on the antenna and are gathered in the receiver placed in its focus, thus increasing considerably the input capacity. In other words, the parabolic antenna works as an amplifier, or even better as a condenser of signals, otherwise too feeble, coming from satellites.

What happens with the hyperbole is slighly more complicated. If we stand on the outside, a ray directed to one focus is reflected in the direction of the other focus. On the inside, a ray provening from from one focus, after a reflection on the hyperbole will seem to provene from the other focus.