已知m>1,直线l：x-my-m^2/2=0椭圆C：x^2/m^2+y^2=1,F1、F2分别为椭圆的左右焦点
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1.直线l：x-my-m^2/2=0 y=0 x=m^2/2
直线l过右焦点F2时 c=m^2/2 m^4/4=m^2-1 (m^2/2-1)^2=0 m^2=2 m=√2
直线l的方程 x-√2y-1=0
2.A(x1,y1) B(x2,y2)
x-my-m^2/2=0 x=my+m^2/2
x^2/m^2+y^2=1 x^2=m^2-m^2y^2
2y^2+my+m^2/4-1=0
y1y2=m^2/8-1/2 y1+y2=-m/2
x-my-m^2/2=0 x=my+m^2/2
x1x2=m^2y1y2+m^3/2(y1+y2)+m^4/4
向量OA*向量OB=x1x2+y1y2=m^4/8-m^2/2-m^4/4+m^4/4+m^2/8-1/2
=m^4/8-3m^2/8-1/2=7/4
m^4-3m^2-18=0
m^2=6或m^2=-3(舍)
所以m^2=6
椭圆方程
x^2/6+y^2=1
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