近日,我借助几何画板发现了圆锥曲线的一个有趣性质,介绍如下,并用不同的方法分别给出证明.性质1)如图1所示,在椭圆中,F为其一个焦点,l为其对应的准线,长轴的两个端点为A1,A2,P是椭圆上异于A1,A2的任一点,设A1P交l于M,PA2交l于N,则MF⊥NF.2)如图2所示,在双曲线中,F为其一个焦点 Recently, I found an interesting property of the conic section with the help of the Geometry Sketchpad. It was introduced as follows and proved by different methods. Properties 1) As shown in Figure 1, in the ellipse, F is a focal point, and l is its counterpart. The two ends of the long axis are A1, A2, P are any points on the ellipse that are different from A1, A2. Let A1P intersect l to M, PA2 intersect l to N, then MF⊥NF.2) 2 shows that in the hyperbola, F is a focus