In parabola, let the equation of parabola be y 2 = 2px (P >; 0), the coordinate of the focus f is (p, 0), and the equation of the directrix is x =-p. If A(x 1, y 1) is any point on the parabola, AF is the distance from point A to the focus, and AF' is the distance from point A to the directrix. According to the definition of parabola, AF is equal to the distance from point A to the alignment, that is, AF = AF'.
If B(x2, y2) is another point on the parabola, BF is the distance from point B to the focus, and BF' is the distance from point B to the collimation line. Similarly, BF is equal to the distance from point B to the line shape, that is, BF = BF'. For any two points A and B on the parabola, there are AF=AF' and BF=BF', which means that the distance from the point on the parabola to the focus is equal to the distance from the directrix.
This theorem is very useful in solving problems related to parabola. For example, when solving the length problem related to a chord on a parabola, the length of the chord can be calculated by this theorem. In addition, this theorem can also be used to prove some geometric properties and theorems related to parabola.
Parabola is very important in mathematics and physics;
1. It describes a curve in which the distance from any point to a fixed point and a fixed straight line is equal. This fixed point is called focus, and the fixed straight line is called directrix.
2. In mathematics, parabola is a kind of quadratic curve, which can be used to solve many different types of mathematical problems, such as solving equations, optimizing problems and proving inequalities. Parabolic equations can also be used to describe physical phenomena such as optics, mechanics and acoustics.
3. In physics, parabola is widely used in the calculation of range and trajectory. For example, the shooting of shells and rockets needs to know their trajectories in the air, and this trajectory is a parabola. Using parabolic equation and physical parameters, the range and trajectory of shells or rockets can be calculated.
4. Parabola has applications in other fields, such as engineering, economics and computer science. For example, in computer graphics, parabola is used to draw various curves and surfaces; In economics, parabola is used to describe the changing laws of some economic phenomena.