Description of the conics in vector algebra terms made use a quantity called e.
Given a directrix line L and a focus point F not on L, a conic section is a set of points X satisfying
where e is a positive real number called the eccentricity and is the distance from X to L. The conic is an ellipse if , a parabola if , and a hyperbola if .
Now, given a point P on L, we can write
where is the unit normal vector of L. Hence, (2.20) can be written as
This can be simplified by setting , where d is the distance between F and L [see Fig.2.12]. Thus,