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 |).
The focal length of an ellipse is the first definition of an ellipse:
Among them, two fixed points F 1 and F2 are called the focal points of an ellipse, the distance between the two focal points │F 1F2│=2c, and the focal length =2c.
Extended data:
In the standard equation of ellipse x 2/a 2+y 2/b 2 =1,if a >:b>；; 0 the focus is on the x axis; If the b>a> focus is on the y axis. At this time, a stands for the major axis and b stands for the minor axis.
C represents half the distance between two focal points, and there is a 2 = c 2+b 2.
Eccentricity e=c/a
(0<e< 1), the larger e, the flatter the ellipse. Eccentricity of ellipse is 0.
Parametric equation of ellipse x=acosθ.
y=bsinθ.
When solving the maximum distance from a point on an ellipse to a fixed point or a fixed line, the problem can be transformed into a trigonometric function problem by solving x=a×cosβ with parametric coordinates.
y=b×sinβ
A is half the length of the spindle.
B is half the length of the minor axis.
References:
Baidu encyclopedia-ellipse