This is a question of determining the chords of the score. Let the linear equation be x = √ 3+t and y = kt.
Combining with elliptic equation ①, and sorting, we get
(4k？ + 1)t？ +2√3t- 1=0 ……②
According to vector AF=3 and vector FB, there is tA=-3tB, which is obtained by combining with ②.
(-2√3-√△)/[2(4k？ + 1)] = -3 (-2√3+√△)/[2(4k？ + 1)]
Simplify with delta = 4 (2 √ 3)?
That is 12+4(4k? + 1)=4 12
Solve k? =2, because k>0, so k=√2.