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# parametre

*Parametre* means often a quantity which is considered as constant in a certain situation but which may take different values in other situations; so the parametre is a “variable constant”. But in giving a curve or a surface in parametric form, the parametres work as proper variables which determine the values of the coordinates of the points; then we can describe the parametres as “auxiliary variables”.

$\displaystyle\begin{cases}x=a\cos{t}\\ y=a\sin{t}\end{cases}$ |

of the origin-centered circle contains both above-mentioned sorts of parametres: $a$ (the radius) is a variable constant which is held constant all the time when one considers one circle; $t$ is an auxiliary variable which has to get all real values (e.g. from the interval $[0,\,2\pi]$) for obtaining all points of the perimetre.

In the analytic geometry, one speaks of the *parametre of parabola* (a.k.a. *latus rectum*): it means the chord of the parabola which is perpendicular to the axis and goes through the focus; it is the quantity $2p$ in the standard equation $x^{2}=2py$ of the parabola ($p$ is the distance of the focus and the directrix).

## Mathematics Subject Classification

00A05*no label found*

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