当抛物线的弦所在直线过定点时,抛物线对称轴上一点与弦的两个端点形成的直线斜率或夹角的平分线有一定的规律,本文就此作一探究,给出三条性质(及其逆性质)并举例说明其应用.性质1抛物线C:y~2=2px与直线y=k(x-m)交于A,B两点,O是坐标原点,则k_(OA)·k_(OB)=-(2p/m).证明设A(x_1,y_1),B(x_2,y_2),则 When the line where the parabolic chord is located passes a fixed point, there is a certain law of the bisector of the slope or angle formed by the two ends of the parabola on the axis of symmetry of the parabola. This article makes an exploration of the three properties (and their inverse (OA) · k OB (OB) = 0, and its application is given by way of example. Property 1 Parabola C: y ~ 2 = 2px and the line y = k - (2p / m). Prove that A (x_1, y_1), B (x_2, y_2), then