解题方法
1 . 已知双曲线
,上顶点为
,直线
与双曲线
的两支分别交于
两点(
在第一象限),与
轴交于点
.设直线
的倾斜角分别为
.
(1)若
,
(i)若
,求
;
(ii)求证:
为定值;
(2)若
,直线
与
轴交于点
,求
与
的外接圆半径之比的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7bcb34ed3bf1981b04d07b53030264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342ba1917a6b854ad111a3e6f5514934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d5467e6dd66a263e3b8607385c2acf.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71885f023172807ad43f2c9a670aa960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093c05ac99b784f79ab03edb81bdc8c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554bc87180cd813a4c5d4eb88996d089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847a4906dd3bb720f3c340cea2d297dc.png)
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