Abstract: To deeply dig the extended properties of a rational quadratic Bézier curve out of 0,1,this paper used the standard form of the curve and studied the limitation when the parameter tends to ∞.It firstly calculated the position of the limit point.Then it separately considered the limit properties under the case of ellipse and hyperbola from comparing the positions of the existing points and the limit point,working out the zeroes of the denominator of the rational form,and considering the tangent direction at the limit point.The example results show that the limit point is collinear with the elliptical center and the shoulder point,the tangent direction at the limit point parallelizes the line between two end control points,the limit point can be regarded as a control point of the extended curve and used for the representation of the whole ellipse,and so on.