1 . 已知点
为双曲线
上任一点,
为双曲线的右焦点,过
作直线
的垂线,垂足为A,连接
并延长交y轴于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/6eb70376-cd94-4cc1-a517-ee193669a6df.png?resizew=238)
(1)求线段
的中点
的轨迹
的方程;
(2)已知
,过点
的直线l与轨迹E交于不同的两点M、N,设直线DM和直线DN的斜率分别为
和
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15be73296477fc390f8b438cfd52b452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5fd9b17a0ed5508c11547ea3fbb3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f1b40221f57567c67c1ba5ceb2f57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfa8bf45e6d2d25a730a793d0cf5694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31889f8671f76ca924c9d86f6fdc929c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ec9341909c0edd74ee755543c4c35.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/6eb70376-cd94-4cc1-a517-ee193669a6df.png?resizew=238)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10195cb8bc3cb0db5c76dd15d331a28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85acf3c73db7fad56a34b1f86f5bdbf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb1b7b68a0fcb11f39395f57cba1c27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2562424a83aae7e4b3f8adf90307961a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b58edb637c5dfa03794f3952de9d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8869f1b1c62e8e88f528a38d6d71968a.png)
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2022-10-21更新
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473次组卷
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3卷引用:河南省驻马店市确山县第一高级中学2022-2023学年高二上学期数学竞赛试题