Focus

The fixed point is called focus, denoted as F1 (ae, 0).

Directrix

The fixed line is called directrix of the ellipse and its equation is x = a/e.

Major Axis

The line segment AA′ is called the major axis and the length of the major axis is 2a. The equation of the major axis is y = 0.

Minor Axis

The line segment BB′ is called the minor axis and the length of minor axis is 2b. Equation of the minor axis is x = 0.

The length of major axis is always greater than minor axis.

Centre

The point of intersection of the major axis and minor axis of the ellipse is called the centre of the ellipse. C(0, 0) is the centre of the ellipse. The centre need not be the origin of the ellipse always.

End points of latus rectum and length of latus rectum

If L1 and L1′ are the end points of the latus rectum, then

L1 = (ae, b2/a)

L1′ = (ae, −b2/a)

The length of the latus rectum is 2b2/a.

Vertices

The points of intersection of the ellipse and its major axis are called its vertices. The vertices of the ellipse are A(a, 0) and A′(−a, 0).

Focal Distance

The focal distance with respect to any point P on the ellipse is the distance of P from the referred focus.

Focal Chord

A chord which passes through the focus of the ellipse is called the focal chord of the ellipse.

Latus Rectum

It is a focal chord perpendicular to the major axis of the ellipse. The equations of latus rectum are x = ae, x = −ae.

Focal Property of Ellipse

The sum of the focal distances of any point on an ellipse is constant and is equal to the length of the major axis.

F1P + F2P = 2a