Question

椭圆x2/a2+y2/b2=1的两个焦点F1,F2的距离之比PF1:PF2=2:根号3,且∠PF1F2=a（0＜a＜π/

Answer 1

│PF1│+│PF2│=2a ,2a为长轴长

又│PF1│：│PF2│=2：根号3

∴│PF1│=4a/(2+根号3) ,│PF2│=2根号3a/(2+根号3)

2│PF1│·│F1F2│cos∠PF1F2=│PF1│^2+│F1F2│^2-│PF2│^2=(4a/(2+根号3) )^2+(2c）^2-(2根号3a/(2+根号3) )^2

∴ 2·4a/(2+根号3) ·2c·cos∠PF1F2=4c^2+4a^2/(2+根号3)^2

∴cos∠PF1F2=(4c^2+4a^2/(2+根号3)^2)/(16ac/(2+根号3))=(e^2+1/(2+根号3)^2)/(4e/(2+根号3))≥