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

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).