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Parameter
Parameter means often a quantity which is considered as constant in a certain situation but which may take different values in other situations; so the parameter is a “variable constant”. But in giving a curve or a surface in parametric form, the parameters work as proper variables which determine the values of the coordinates of the points; then we can describe the parameters as “auxiliary variables”.
The parametric presentation
 |
(the radius) is a variable constant which is held constant all the time when one considers one circle; 
is an auxiliary variable which has to get all real
values (e.g. from the interval
![$ [0,\,2\pi]$](http://myyn.org/static/assets/mathbrowser/article/5073/images/img4.png){kind=small}
) for obtaining all points of the perimetre.
In the analytic geometry, one speaks of the parameter of parabola: it means the chord
of the parabola
which is perpendicular
to the axis
and goes through the focus; it is the quantity 
in the standard equation
of the parabola (
is the distance
of the focus and the directrix).