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Ellipse


Ellipse Definition

An ellipse is the set of all points which moves in a plane in such a way that the addition of its distance from two fixed points in the plane is a constant.
The two fixed points are called the foci of the ellipse.

what is Ellipse
In the given figure, F1 and F2 are two fixed points and P is a points which moves in such a way that

PF+ PF= constant.

Major and Minor Axes

The line segment through the foci of the ellipse with is end point on the ellipse. This is called its major axis.

In the given figure , AB is the major axes of the ellipse.

Length of the major axis = AB =2a.

Major and Minor Axes

Minor Axis

The line segment thought the center and perpendicular of the major axis with its end point of the ellipse. This is called its minor axis.

In the given figure, CD is the minor axis of the ellipse.

Length of the Minor axis =CD =2b.

 

Eccentricity of the Ellipse

Eccentricity of the Ellipse

Since for an ellipse, c ≤ a the eccentricity is always < 1.

Standard Equation of Ellipse

Equation of Ellipse

where a and b are the length of the semi-major axis and the semi-minor axis and a>b.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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