The standard equation of Lele classroom ellipse is: x 2/a 2+y 2/b 2 =1,(a>b>0); When the focus is on the Y axis, the standard equation of the ellipse is: Y 2/A 2+X 2/B 2 =1,(a>b>0).

First, the concept of ellipse:

In mathematics, an ellipse is a curve around two focal points on a plane, so for each point on the curve, the sum of the distances to the two focal points is constant. Therefore, it is a generalization of a circle, and it is a special type of ellipse with two focuses at the same position.

The shape of an ellipse (how to "stretch") is expressed by its eccentricity, which can be any number from 0 (the limit case of a circle) to close to but less than 1.

An ellipse is a closed cone section: a plane curve intersects a plane through a cone. There are many similarities between the other two forms of ellipse and cone section: parabola and hyperbola, which are both open and unbounded. The cross section of a cylinder is elliptical unless it is perpendicular to the axis of the cylinder.

Second, the introduction of ellipse:

An ellipse can also be defined as a set of points, so that the ratio of the distance between each point on the curve and a given point (called focus) to the distance between the same point on the curve (called directrix) is a constant. This ratio is called eccentricity of ellipse.

Ellipses can also be defined in this way. An ellipse is a collection of points, and the sum of the distances from these points to two focal points is a fixed number.

Application of ellipse

1. astronomy:

The orbits of planets and celestial bodies are usually elliptical, and Kepler's law of elliptical orbit describes this phenomenon. These laws are very important for understanding and predicting the motion of celestial bodies.

2. Navigation:

Elliptical projection of the earth's surface is used to make maps. Elliptic projection is helpful to accurately represent the curve of the earth's surface on a plane map.

3. Satellite communication:

Satellite orbits are usually elliptical, which enables satellites to cover different areas and keep a relatively constant distance. This kind of orbit design is very important for satellite communication.

4. Engineering design:

Ellipse is used in many engineering designs, such as automobile tires, water tanks, lenses and so on. Ellipse has the characteristics of uniform distribution, which can be used to improve the strength and performance of the structure.

5. Astronomical mirrors and parabolic mirrors;

Some astronomical telescopes and parabolic mirrors use elliptical lenses or mirrors to focus light.