直线斜率不存在时,S△ABF2=2,不满足
x^2/4+y^2/2=1
y=kx
联立得:(2k^2+1)x^2-4=0
设A(x1,y1),B(x2,y2)
S△ABF2=1/2|y1-y2|·|OF2|
=√2|y1|
=√2|k||x1|
=2√2|k|/√(2k^2+1)
=√3
k^2=3/2
所以直线方程为y=±√6/2x
(结果不知对不对,思路没错)
直线斜率不存在时,S△ABF2=2,不满足
x^2/4+y^2/2=1
y=kx
联立得:(2k^2+1)x^2-4=0
设A(x1,y1),B(x2,y2)
S△ABF2=1/2|y1-y2|·|OF2|
=√2|y1|
=√2|k||x1|
=2√2|k|/√(2k^2+1)
=√3
k^2=3/2
所以直线方程为y=±√6/2x
(结果不知对不对,思路没错)