惠润科老师在文[1]中给出圆锥曲线的如下性质:过圆锥曲线焦点F作倾斜角为α的直线l与圆锥曲线交于A,B两点,且F分AB所成比为λ,e为离心率,则cos2α=e(2(λλ-+11))22.原证明采用传统解析几何的方法,但证明过程较繁琐.笔者利用圆锥曲线的第二定义,并采用数形结合的方法,给出该性 Hui Runke teacher in the paper [1] gives the following properties of the conic: over the conic F focal point for the tilt angle α for the straight line l and conic at the intersection of A and B, and F points AB ratio λ, e is the eccentricity, then cos2α = e (2 (λλ- + 11)) 22. The original proof using the traditional analytical geometry method, but the process proved more cumbersome. I use the second definition of the conic curve, The method of combining gives this