椭圆 急救

设P(acosm,nsinm)
则向量PF1·向量PF2=a^2(cosm)^2+b^2(sinm)^2-c^2
=(a^2-b^2)(cosm)^2+b^2-c^2
最大值是(cosm)^2=1的时候取到，是a^2-b^2+b^2-c^2=a^2-c^2
所以c^2<=a^2-c^2<=3c^2
2c^2<=a^2<=4c^2
1/2<=e<=二分之根号2

向量PF1·向量PF2
=|PF1|*|PF2|cosθ为这两个向量的夹角)
<=|PF1|*|PF2|
<=[(|PF1|+|PF2|)/2]^2
=a^2
||||θθθθ
向量PF1·向量PF2的最大取值范围是[c^2,3c^2],
则有c^2<=a^2<=3C^2,得1/3c^2<=1/a^2<=1/c^2
即1/3<=e^2<=1,√3/3<=e<=1,由a>b知e不等于1

故椭圆C的离心率e的取值范围是[√3/3,1)