研究发现,定点到有心圆锥曲线焦点的距离与过该定点的切线的切点焦半径存在着美妙的等量关系.定理1已知F1、F2分别是椭圆的两个焦点,过椭圆外任意一点P向椭圆引切线,A、B是切点.求证:|PF1|2|PF2|2=|AF1|·|BF1||AF2|·|BF2|.分析利用点P的切点弦方程和椭圆方程求出切点A、B坐标满足的方程,利用韦达定理求出切点横坐标的关系,然后利用椭圆的焦半径公式进行 It is found that there is a wonderful equivalence relationship between the distance from the fixed point to the focal point of the concentric curve and the focal point of the tangent point passing the fixed point. Theorem 1 It is known that F1 and F2 are the two focal points of the ellipse respectively. P to the elliptic tangent, A, B is the tangent point. Confirmation: | PF1 | 2 | PF2 | 2 = | AF1 | · | BF1 | | AF2 | · | BF2 | The equations are obtained for the points A and B that satisfy the co-ordinates. The relationship between the abscissa and the co-ordinates of the point of contact is determined using the Vedic theorem, and then the coherence radius of the ellipse is used