First, common secondary conclusions:

1. The eccentricity of an ellipse is defined as the ratio of the focal length to the major axis of the ellipse (range: 0: 2c). The greater the eccentricity, the flatter the ellipse. The smaller the eccentricity, the closer the ellipse is to the circle.

2. The focal length of the ellipse: the distance between the focal point of the ellipse and its corresponding directrix (such as focal point (c, 0) and directrix X = A 2/c-C = B 2/c) is A 2/c.

3. The focus is on the X axis: | pf1| = a+ex | pf2 | = a-ex (f1,f2 is the left and right focus respectively).

4. The radius of ellipse passing through the right focus is r=a-ex.

5. The radius of the left focus is r=a+ex.

Second, the meaning of the ellipse:

An ellipse is the trajectory of a moving point P. The sum of the distances from the moving point P to the fixed points F 1 and F2 in a plane is equal to a constant (greater than |F 1F2|), and F1and F2 are called the two focuses of the ellipse. The mathematical expression is | pf1|+pf2 | = 2a (2a > | f1F2 |).

Application field of ellipse

First of all, the field of mathematics

1, Geometry: Ellipse is a plane figure. Through its geometric properties, we can study and solve geometric problems related to ellipses, such as eccentricity, focus and symmetry of ellipses.

2. Analytic geometry: Ellipse plays an important role in analytic geometry. They are used to describe the characteristics of curves and graphs and the relationship between them.

3. Calculus: Elliptic curves are widely used in calculus, especially in the calculation of integral and derivative of curves.

4. Linear Algebra: Ellipse has many applications in linear algebra, such as matrix representation and matrix operation of elliptic equations.

Second, the field of physics.

1. optics: the fluctuation of light can be described as elliptical vibration in space, and elliptical polarization is an important concept in optics.

2. Astrophysics: The orbits of planets and satellites are usually elliptical, so it is necessary to study and describe their trajectories with the theory of ellipses.

3. Electromagnetic field: The propagation and diffraction of electromagnetic wave can also be described and calculated by the parameters of ellipse.

4. Mechanics: Ellipse also has important applications in mechanics, such as the simulation and analysis of planetary motion.