  In this paper, we propose a linear method for $C^{(r,s)}$ approximation of
rational B\'{e}zier curve with arbitrary degree polynomial curve. Based on
weighted least-squares, the problem be converted to an approximation between
two polynomial curves. Then applying Bernstein-Jacobi hybrid polynomials, we
obtain the resulting curve. In order to reduce error, degree reduction method
for B\'{e}zier curve is used. A error bound between rational B\'{e}zier curve
and B\'{e}zier curve is presented. Finally, some examples and figures were
offered to demonstrate the efficiency, simplicity, and stability of our
methods.
