过横轴椭圆焦点直线与椭圆交点与另一焦点形成的三角形面积最大值为6求椭圆方程

s=(1/2)*(2c)|y1-y2|=c*|y1-y2|
s(max)=6
设y1>y2
c=y1-y2=√6
a^2=6+b^2
F(-√6,0)
L:y=k*(x+√6)
b^2*x^2+(6+b^2)*y^2=(6+b^2)*b^2
b^2*x^2+a^2*k^2*(x+√6)^2=a^2*b^2
(b^2+6k^2+b^2*k^2)x^2+2√6a^2*k^2*x+6(6+b^2)*k^2-(6+b^2)*b^2=0
x1= x2=
y1= y2=
y1-y2=√6.(1)
√[(x1+√6)^2+(y1)^2]+√[(x1-√6)^2+(y1)^2]=2a=2√(6+b^2).(2)
(1),(2)
b^2= a^2=6+b^2