解题方法
1 . 双曲线
:
,
的左右焦点分别为
,
,其中双曲线
的一条渐近线方程为
,
为双曲线上一点,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/2e4686fb-c70c-4aa3-bb5c-bfeb02a301fd.png?resizew=179)
(1)求双曲线的方程.
(2)A,
为双曲线左右顶点,过
作一条直线交双曲线于
,
,设
,
的斜率为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b59d842135155be79f9191fc4ff23e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25869dd14f3e7412beda491bb83f982d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1f951d4fe9ce1edd150b985b95df5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f47c6b79bcc4bb4e3fb264c12d09c2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/2e4686fb-c70c-4aa3-bb5c-bfeb02a301fd.png?resizew=179)
(1)求双曲线的方程.
(2)A,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
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解题方法
2 . 已知双曲线
的左右焦点分别为
,
,M在C的右支上,
的最大值为3,且当
时,
的面积为
.
(1)求C的方程;
(2)若A,B是C上位于x轴上方上的两点,且
,
与
交于点P,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14503fb4f0ee53847732c298c13db666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055d142537abd9027651859f62661fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480308829702eaffa5b095819187c40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f9a699aededce0ad803bf8257fbbcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
(1)求C的方程;
(2)若A,B是C上位于x轴上方上的两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d4f42c799e2845340f8726ed39a2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe1cad1ce47339827ac5047af4647d.png)
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