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**Unformatted text preview: **In this subsection, we start from scratch to reintroduce the conic sections from a more uniﬁed
perspective. We have our ‘new’ deﬁnition below.
Definition 11.1. Given a ﬁxed line L, a point F not on L, and a positive number e, a conic
section is the set of all points P such that
the distance from P to F
=e
the distance from P to L
The line L is called the directrix of the conic section, the point F is called a focus of the conic
section, and the constant e is called the eccentricity of the conic section.
We have seen the notions of focus and directrix before in the deﬁnition of a parabola, Deﬁnition 7.3.
There, a parabola is deﬁned as the set of points equidistant from the focus and directrix, giving an
eccentricity e = 1 according to Deﬁnition 11.1. We have also seen the concept of eccentricity before.
It was introduced for ellipses in Deﬁnition 7.5 in Section 7.4, and later in Exercise 7 in Section 7.5.
There, e was also deﬁned as a ratio of distances, though in these cases the dist...

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