在一些平面解析几何的教科书和习题集里,常有关于圆锥曲线的这样一个命题:过圆锥曲线C的焦点F,作该圆锥曲线C的弦PQ,则: 1/FP+1/FQ=2/ep(e是圆锥曲线C的离心率,p为焦参数。) 常看到这样的证法:(简称证法(1)) 以焦点F为极点,极轴垂直于准线,且以准线到焦点的方向为其正向,建立极坐标系,则圆锥曲线方程为: ρ=ep/1-ecosθ如图(1),设P点的坐标为(ρ_1,θ_1),则Q点的坐标为(ρ_2,π+θ_1)于是 In some textbooks and problem sets of plane analytic geometry, there is often a proposition about the conic curve: the focal point F of the conic curve C, the chord PQ of the conic curve C, then: 1/FP+1/FQ=2 /ep(e is the eccentricity of conic curve C, p is the coke parameter.) This proof method is often seen: (Proof method (1)) With the focal point F as the pole, the polar axis is perpendicular to the guideline, and The line-to-focus direction is its positive direction. To establish a polar coordinate system, the conic curve equation is: ρ=ep/1-ecosθ (1), set the P point coordinate to (ρ_1,θ_1), then the Q point The coordinate is (ρ_2,π+θ_1)