Question

椭圆x2/4+y2=1的右焦点为F,A,B,C为该椭圆上的三点,若FA+FB+FC=0(向量),则|FA|+|FB|+|FC|=___

Answer 1

a=2 & c^2=4-1=3, e=c/a=根号3/2 A（x1,y1)，B（,x2,y2)，C（x3,y3)
则：向量FA+FB+FC=（x1-c+x2-c+x3-c，y1+y2+y3)=0(向量),
所以 x1-c+x2-c+x3-c=0， x1+x2+x3=3c
|FA|+|FB|+|FC|=a-ex1+a-ex2+a-ex3=3a-e(x1+x2+x3)=6-9/2=3/2

Answer 2

a=2 & c^2=4-1=3, e=c/a=根号3/2 A（x1,y1)，B（,x2,y2)，C（x3,y3)
则：向量FA+FB+FC=（x1-c+x2-c+x3-c，y1+y2+y3)=0(向量),
所以 x1-c+x2-c+x3-c=0， x1+x2+x3=3c
|FA|+|FB|+|FC|=
=6-9/2=3/2