Definitions
Any conic section can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio. That ratio is called eccentricity, commonly denoted as "e."
The eccentricity can also be defined in terms of the intersection of a plane and a double-napped cone associated with the conic section. If the cone is oriented with its axis being vertical, the eccentricity is
where α is the angle between the plane and the horizontal and β is the angle between the cone and the horizontal.
The linear eccentricity of a conic section, denoted c (or sometimes f or e), is the distance between its center and either of its two foci. The eccentricity can be defined as the ratio of the linear eccentricity to the semimajor axis a: that is, .
Read more about this topic: Eccentricity (mathematics)
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