The eccentricity of a conic section is a parameter that encodes the type of shape and is defined in terms of semimajor 
and semiminor
axes 
as follows.
The eccentricity can also be interpreted as the fraction of the distance along the semimajor axis at which the focus lies,
 |
(1)
|
where 
is the distance from the center of the conic section
to the focus.
The term "eccentricity" is also used in geodesy to refer to one of a number of similar quantities characterizing a spheroid. Given
a spheroid with equatorial radius 
and polar semi-axis 
, this (first) eccentricity, commonly denoted 
(Snyder 1987, p. 13; Karney 2023) but sometimes also
as 
(Beyer 1987, p. 131), is defined
as
 |
(2)
|
As a result of the definition, the eccentricity 
is positive for an oblate spheroid
and purely imaginary for a prolate
spheroid. Additional (second and third) eccentricities are defined as
 |
(3)
|
and
 |
(4)
|
(Karney 2023).
