For the elliptic standard equation (focusing on the X axis), x 2/a 2+y 2/b 2 =1(a > b > C a is the semi-major axis b is the semi-minor axis c is half the focal length), and the corresponding directrix equation.

X = a 2/c (focus (c，0))

X =-a 2/c (focus (-c, o))

Let the alignment be x = f.

Then the distance l from a to a straight line is f-X.

Let af1/l = e.

(x-c)？ +y？ =e？ (f-x)？

Simplify (1-e? )x？ -2xc+c？ +y？ -e？ f？ +2e？ fx=0

Make 2c=2e? f

So f=c/e?

Let this point be the right vertex rule (c/e? -a)e=a-c

When e=c/a, the above formula holds.

So f=a? /c

The equation is (1-e? )x？ +y？ =e？ f？ -c？

Introduction to 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 parallel to the axis of the cylinder.