一、问题的提出如图1,在椭圆x~2/a~2+y~2/b~2=1(a>b>0)中,F_1、F_2分别是左、右焦点,点P是椭圆上任一点,对于焦点△PF_1F_2中的两条焦半径PF_1,PF_2,现有的研究已比较深入,我考虑延长PF_1交椭圆于点Q,延长PF_2交椭圆于点M,把两条焦半径的问题拓展为四条焦半径PF_1,PF_2,QF_1,MF_2的问题.由于点P是动点,所以 First, the problem proposed in Figure 1, in the elliptic x ~ 2 / a ~ 2 + y ~ 2 / b ~ 2 = 1 (a> b> 0), F_1, F_2 are left and right focus, the point P is At any point on the ellipse, for the two focal radii PF_1 and PF_2 in the focal point △ PF_1F_2, the existing researches are more in-depth. I consider extending the intersection of PF_1 and the ellipse at point Q, extending the intersection of PF_2 and ellipse at point M, The problem is expanded to the four focal radius PF_1, PF_2, QF_1, MF_2 problem. Since the point P is the moving point,