parametreParameter2007-05-21 01:49:122009-08-07 09:04:05Definitionvariableauxiliary variableparametric formparametric presentationparameter of parabola% this is the default PlanetMath preamble. as your knowledge
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\PMlinkescapeword{constant}
\emph{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 {\em 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''.
The parametric \PMlinkescapetext{presentation}
\begin{align*}
\begin{cases}
x = a\cos{t}\\
y = a\sin{t}
\end{cases}
\end{align*}
of the origin-centered circle \PMlinkescapetext{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 \emph{parametre of parabola} (a.k.a. \emph{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).