What is the alignment equation of an ellipse?

The alignment is used to draw an ellipse, so there is no such line on the diagram. When learning the ellipse, there is a principle I don't know if the landlord remembers, as shown in the figure, two points (f1, f2) are connected by a rope, take the third point p on the rope casually, tighten the rope to make a circular motion at the vertex p, and the trajectory obtained is both an ellipse.

A collimation is a straight line perpendicular to the x-axis through two focal points. (a>b)

On the contrary, a <>

There are two ways to draw an ellipse: geometric and algebraic.

The first type: geometric method.

It is the first definition of an ellipse, which is the one learned in the book, and the sum of the distances to two fixed points.

The second: algebraic method.

It is the second definition of an ellipse, the collimation is derived from the algebraic method, and the ellipse can be drawn with a collimation and a fixed point! Namely.

Distance to fixed point Distance to fixed line = constant e

A collection of points.

It's an ellipse! The fixed line here is the alignment. Now that you know what the alignment is, just memorize the alignment formula y=+ or -a 2 c

When the ratio of the distance from the moving point p to the fixed point f (focus) and to the fixed line x=xo is the eccentric rate, the straight line is the intensity of the ellipseAlignment

Conic. The ratio of the distance from any point to a focal point and its corresponding alignment (the focal point and the alignment on the same side of the y-axis) is the eccentricity.

The ratio of the distance from any point on the ellipse to the focal point to the distance from that point to the corresponding alignment is equal to the eccentricity e.

In the uniform definition of conic curves:

The trajectory of a point where the ratio of the distance to the fixed point to the fixed line is the constant e (e is greater than 0).

It is called a conic curve, and this definite line is called the alignment b (b is greater than 0).

Define the open bridge: the ratio of the distance to the focal point to the distance to the alignment of all points on the ellipse is the fixed carrying value.

Alignment equation: x=a2 c, x=-a2c.

The coordinates of point p on the ellipse (x0, y0) 0 When the ratio of the distance from the moving point p to the fixed point f (focus) and to the fixed line x=xo is the eccentric rate, the line is the alignment of the ellipse.

Alignment equation: x=a2 c, x=-a2c.

For the elliptic equation (taking the focus on the x-axis as an example) x 2 a 2+y 2 b 2=1 (a>b>0 a is the major semi-axis, b is the minor semi-axis, and c is half of the focal length) (it can also be defined as: when the ratio of the distance from the moving point p to the fixed point f (focal point) and the fixed line x=xo is the eccentricity, the line is the alignment of the ellipse. ）

Alignment: For the elliptic equation (take the focus on the x-axis as an example) x 2 a 2+y 2 b 2=1 (a>b>0, a is the major semi-axis, b is the minor semi-axis, and c is half of the focal length).

An ellipse is a curve in a plane that surrounds two focal points such that for each point on the curve, the sum of the distances to the two foci is constant. Therefore, it is a generalization of a circle, which is a special type of ellipse with two focal points at the same position.

Hello! Glad for your question!

Answer: When the ratio of the distance from the moving point p to the fixed point f (focus) and to the fixed line x=xo is the eccentric rate, the straight line is the alignment of the ellipse.

Alignment equations: x=a c and x=-a c.

Yours is the greatest support to me! Break a leg! Thank you!

The alignment equation for an ellipse looks like this:

x-h)^2/a^2 + y-k)^2/b^2 = 1

where (h,k) is the central coordinate of the ellipse, a is the length of the major semiaxis of the ellipse, and b is the length of the minor semiaxis of the ellipse.

There are two collimation equations for an ellipse.

x=a2c and x=-a2c. The ratio of the point on the ellipse to the focal point and the distance of the focal point corresponding to the alignment (i.e., the one that is close) is the eccentricity, which is the second definition of an ellipse.

First of all, it depends on the position of your ellipse, such as the x-axis of the major axis, the position on the y-axis, the center of the ellipse, and so on. Different alignments are not the same. In addition, the alignment is also related to the amount of ellipse.

The equation for the ellipse x a + y b = 1

The alignment equation is: y= a c

Again, the focus is on the y-axis, and the principle is the same.

x=a2 c, outside the ellipse, the elliptic equation can be solved using the alignment, and the ratio of the distance from any point on the ellipse to the focal point to the distance from that point to the corresponding alignment is equal to the eccentricity e