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轴相交,故斜率存在,设直线l方程为y=kx-1,求得l与y轴交于M0,-k,又F坐标为10,设l交椭圆于Ax1,y1,Bx2,y2,
y=kx-1,由x2y24+3=1,
消去y得3+4k2x2-8k2x+4k2-12=0,4k2-128k2∴x1+x2=,x1x2=,3+4k23+4k2→→又由MA=λAF,∴x1,y1+k=λ1-x1,-y1,x1x2∴λ=,同理μ=,1-x11-x2x1+x2-2x1x2x1x2∴λ+μ=+=1-x11-x21-x1+x2+x1x224k2-128k2-3+4k23+4k2
22

8=-34k-128k1-+3+4k23+4k2
8所以当直线l的倾斜角变化时,直线λ+μ的值为定值-3
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