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在平面解析几何中,据定比分点公式易知由P_1,P_2两点所确定的直线P_1P_2(不包括P_2点)的参数方程为: 鉴于参数方程在解决平面解析几何问题上的重要作用,我们对直线的参数方程(*)的应用作如下说明: 例1 在△AEC中,D是BC边上的中点,过D任作直线交AC于E。交AB的延长线于F,求证:AE:EC=AF:BF。证明:如右图所示建立直角坐标系。由直线参数方程
In the plane analytical geometry, according to the definition of the point-of-sequence formula, it is easy to know the parametric equation of the straight line P_1P_2 (excluding the P_2 point) determined by the two points P_1, P_2 as: In view of the important role of the parametric equation in solving the plane analytical geometry problem, we The application of the linear parametric equation (*) will be described as follows: Example 1 In ΔAEC, D is the midpoint on the BC side, and D passes the straight line AC to E. The extension of AB is extended to F. Proof: AE:EC=AF:BF. Proof: Set up the Cartesian coordinate system as shown in the right figure. Parametric Equation