Page 6 - LN

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.

Relationship between semi-major axis, semi-minor axis and the distance of the focus from the centre
of the ellipse:

2
2
a = b + c

2
⇒ c = a − b
Eccentricity: The eccentricity of an ellipse is the ratio of the distances from the centre of the
ellipse to one of the foci and to one of the vertices of the ellipse (eccentricity is denoted by e)
c
i.e., e =
a
Standard equations of an ellipse: The equation of an ellipse is simplest if the centre of the
ellipse is at the origin and the foci are on the x-axis or y-axis.

Note: The standard equations of ellipses have centre at the origin and the major and minor axis are
coordinate axes.