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在椭圆和双曲线中,关于共焦点P的两条焦半径| PF_1|与| PF_2|垂直的充分必要条件是中学数学研究的热点,而对于共焦点F的两条焦半径| FA |与| FB |垂直的研究并不多见,为此,笔者对它作了一点研究,得到了如下一个性质.定理经过原点且倾斜角为θ的直线l与椭圆x~2/a~2+y~2/b~2=1(a>b>0)或双曲线x~2/a~2-y~2/b~2=1(a>0,b>0)相交于A,B两点,F是椭圆或双曲线的焦点,c是半焦距,则(?)·(?)=0的充分必
In ellipse and hyperbola, the necessary and sufficient conditions for the two focal radii | PF_1 | and | PF_2 | about the confocal point P to be perpendicular to the mathematical studies of middle school are the hot spots, and the two focal radii | FA | and | FB | vertical research is rare, for which reason, I made a little research on it, got the following property: Theorem After the origin and the inclination angle θ of the line l and the elliptic x ~ 2 / a ~ 2 + y ~ 2 / b ~ 2 = 1 or hyperbolic x ~ 2 / a ~ 2 ~ y ~ 2 / b ~ 2 = 1 (a> 0, b> 0) , F is the focal point of the ellipse or hyperbola, and c is the semi-focal length, then (?) · (?) = 0