The fixed point is called focus, denoted as F1 (ae, 0).
The fixed line is called directrix of the ellipse and its equation is x = a/e.
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.
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.
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.
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).
The focal distance with respect to any point P on the ellipse is the distance of P from the referred focus.
A chord which passes through the focus of the ellipse is called the focal chord of the ellipse.
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