The mathematical concept of a parabola

The parabola is an infinite curve that consists of points, ravnoudalenie from a given line, called the directrix of the parabola, and a given point - parabola focus. Parabola is a conic section, that is represents the intersection of a plane and a circular cone.

In General, the mathematical equation of the parabola has the form: y=ax^2+bx+c where a is not equal to zero, b represents displacement graph of a function horizontally relative to the origin, and c is the vertical offset of the function relative to the origin. Thus, if a>0, the branches of the parabola in the graph are directed upwards, and in the case that a<0, the flow chart branches of the parabola are directed downwards.

Properties of the parabola

Parabola is a curve of the second order, which has an axis of symmetry passing through the focus of the parabola and perpendicular to the directrix of the parabola.

The parabola has a special optical property, namely, the focus parallel to the axis of symmetry of the light rays directed to the parabola at the vertex of the parabola and defocus of a beam of light directed at the vertex of a parabola, parallel light rays relative to the same axis.

If you produce a reflection of a parabola on any tangent, then the image of the parabola will be at her headmistress. All parabolas are similar among themselves, i.e. for each two points A and B of one parabola, there are points A1 and B1 for which it is the assertion |A1,B1| = |A,B|*k, where k is the coefficient of similarity, which in numerical value is always greater than zero.

Expression of parabola in life

Some cosmic bodies such as comets or asteroids passing near large space objects at high speed have a trajectory in the shape of a parabola. This property of small celestial bodies is used when the gravitational maneuvers of the spacecraft.

For training future astronauts on earth are special flights of aircraft along the trajectory of the parabola, thus achieving the effect of weightlessness in the gravitational field of the earth.

In the home of a parabola can be found in a variety of lighting fixtures. This is due to an optical property of a parabola. One of the last uses of a parabola, based on its self-focusing and defocusing of light rays steel solar panels, which are increasingly included in the scope of supply in the southern regions of Russia.