△AF'F, bottom F'F=2c, when point A is on the Y axis, the height h=b is the largest, and S△AF'F=b*2c/2=bc.
The largest area of AFB triangle is 2000 BC.
2.| u | = |(cosθ+ 1)+I(sinθ- 1)| =√[cos？ θ+2cosθ+ 1+sin？ θ-2sinθ+ 1]
= √[ 2 cosθ-2 sinθ+3]= √[ 2√2 cos(θ+π/4)+3]
∫0≤θ& lt； 2π,
∴ When θ=7π/4, the maximum value of |u| is = √ [2 √ 2+3] = √ [(2)+ 1]? =√2+ 1