a^2=4 b^2=a^2-c^2=4-3= 1

The equation of an ellipse is x 2/4+y 2/1=1.

(2) Let the linear equation be y=kx.

The equivalent elliptic equation is: (1+4k 2) x 2 = 4.

x = 2/√( 1+4k^2)y = = 2k/√( 1+4k^2)

The distance between point A and point B is 4 √ (1+k 2)/√ (1+4k 2).

The height of triangle ABF 1 is (√ 3) k/√ (1+k 2).

The area of triangle ABF 1 is s = (1/2) [4 √ (1+k2)/√ (1+4k2)] [(3) k/√ (1+k2)].

=2(√3)k/√( 1+4k^2)

s'=2(√3)[(√( 1+4k^2))-4k^2/√( 1+4k^2)]/( 1+4k^2)>； 0

The maximum area of triangle ABF 1 is s=√3.