1 . 已知点F为双曲线
的右焦点,过F的任一直线l与
交于A,B两点,直线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/19/56a394b6-6d58-414f-b345-3a058c042d1d.png?resizew=172)
(1)若
为曲线
上任一点,且M到直线
的距离为d,求
的值;
(2)若
为曲线
上一点,直线MA,MB分别与直线
交于D,E两点,问以线段DE为直径的圆是否过定点?若是,求出定点坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997b7f23035c886279a2ce47138f2116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201f83b547c6e4d24ae1b579c62e1ad7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/19/56a394b6-6d58-414f-b345-3a058c042d1d.png?resizew=172)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e976c8bf16c2edc1cfd82f41343271e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4b8587cbcbb5f9627512d504cf09e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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2011·甘肃·二模
解题方法
2 . 已知双曲线
的上、下顶点分别为A、B,一个焦点为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925752b294d622b2386a885ff67382bc.png)
,两准线间的距离为1,
成等差数列.
(1)求双曲线的方程;
(2)设过点
作直线
交双曲线上支于
两点,如果
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29c0738fd840c1acadc91365ff366f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925752b294d622b2386a885ff67382bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8407a79a35b42bd01409c85d2ccf2bc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da5453b3e831fdd33c73bc506c18c5f1.png)
(1)求双曲线的方程;
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfa594f5fd4aa77484bd870820bb78ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbec471ffed534e60ec40d48b9f0968.png)
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