25.(1)F1F2=2c=F2M,F1M=2√3c,
∴(√3-c)^2+a^2=4c^2,(√3+c)^2+a^2=12c^2,
∴a^2=3c^2+2√3c-3=11c^2-2√3c-3,
∴8c^2-4√3c=0,c>0,c=√3/2,
a^2=9/4,b^2=6/4,
∴椭圆方程是x^2/(9/4)+y^2/(3/2)=1.①
(2)设l1:y=kx+n,②
代入①*9,4x^2+6(k^2x^2+2knx+n^2)=9,
整理得(4+6k^2)x^2+12knx+6n^2-9=0,
△/24=6k^2n^2-(2+3k^2)(2n^2-3)=6+9k^2-4n^2>0,n^2