Discussed in this paper the problem of determining a parabola with four orderly points and the effect of the geometric distributing of constrained orderly five points in respect to the shape of conics. A computing method of determining a conic uniquely with five distinct planar points is introduced. The computing translation formulas between implicit conics and rational quadratic Bézier curves are proposed too, and then it is expedient to figure out the parameters of the interpolation knots. Based on this study, a new computational technique of rational re-parameterizations of the constructed knots' parameters is presented. Experiment results show that the error is amended considerably and the interpolating precision is higher with respect to the constructed quadratic curve. Experiments for comparing the efficiency of the two new methods with that of other methods are also included.