题目内容
)已知点
、
和动点
满足:
, 且存在正常数
,使得
(I)求动点
的轨迹
的方程;
(II)设直线
与曲线
相交于两点
、
,且与
轴的交点为
.若
求
的值.


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(I)求动点


(II)设直线








(1)动点
的轨迹
的方程为:
(2)




I)在
中,由余弦定理得


,即动点
的轨迹为以A、B为两焦点的椭圆.
动点
的轨迹
的方程为:
.
(II)由
得
.(※)
设
、
,易知
,则
①
②
又

③
将③代入①、②得
消去
得
或
,代入(※)方程
.故



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




(II)由


设





又



将③代入①、②得


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