Question

已知F1,F2分别是椭圆x^2/8+y^2/4=1的左右焦点,点P是椭圆上的任意一点,则│PF1│.│PF2│=5,则c

Answer 1

│PF1│.│PF2│=5

│PF1│.+│PF2│=2a=4√2,则(│PF1│.+│PF2│)²=│PF1│².+│PF2│²+2│PF1│.│PF2│=32

cos角F1PF2= (│PF1│².+│PF2│²-|F1F2|²)÷ 2│PF1│.│PF2│=(32-2×5-4²)÷(2×5)=3／5