The eccentricity of conic sections formulated as rational Bézier quadratics

The eccentricity of rational quadratic Bezier curves is formulated directly in terms of their control-points and weights. Based on this expression, we analyze the range and extreme values of the eccentricity of conic sections expressed in this form. We also provide an explicit expression for the eccentricity of the osculating conic of a rational Bezier curve of high degree.