(1)直线l:y=(x+3), 由已知c=2及=3,解得a2=6, ∴b2=6-22=2. x2+3y2-6=0,① ∴椭圆方程为+=1. (2) y=(x+3),② 将②代入①,整理得2x2+6x+3=0.③ 设A(x1,y1)、B(x2,y2), 则x1+x2=-3,x1x2=. ∵•=(x1+2,y1)•(x2+2,y2)=(x1+2)(x2+2)+y1y2 =x1x2+2(x1+x2)+4+[x1x2+3(x1+x2)+9]=x1x2+3(x1+x2)+7=0, ∴F1A⊥F1B.则∠AF1B=90°. ∴点F1(-2,0)在以线段AB为直径的圆上. (3)面积最小的圆的半径长应是点F1到直线l的距离,设为r. ∴r==为所求. |