Ellipse

Definition :- An ellipse is the set of all points in

a plane, the sum of whose distances from two

fixed points in the plane is a constant.

The two fixed points are called the foci (plural

of ‘focus’) of the ellipse (Fig11.20).



$Note The constant which is the sum of

the distances of a point on the ellipse from the

two fixed points is always greater than the

distance between the two fixed points.

The mid point of the line segment joining the foci is called the centre of the

ellipse. The line segment through the foci of the ellipse is called the major axis and the

line segment through the centre and perpendicular to the major axis is called the minor

axis. The end points of the major axis are called the vertices of the ellipse





We denote the length of the major axis by 2a, the length of the minor axis by 2b

and the distance between the foci by 2c. Thus, the length of the semi major axis is a

and semi-minor axis is b