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.
In the given figure, F1 and F2 are two fixed points and P is a points which moves in such a way that
PF1 + PF2 = 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.
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
Since for an ellipse, c ≤ a the eccentricity is always < 1.
Standard Equation of Ellipse
where a and b are the length of the semi-major axis and the semi-minor axis and a>b.