名校
解题方法
1 . 已知双曲线
:
的离心率为
,点
在双曲线
上.过
的左焦点F作直线
交
的左支于A、B两点.
(1)求双曲线C的方程;
(2)若
,试问:是否存在直线
,使得点M在以
为直径的圆上?请说明理由.
(3)点
,直线
交直线
于点
.设直线
、
的斜率分别
、
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80cffd36bf06a1feea0e703d1c33eb7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631386549c0cec5981a1da47b05e5d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求双曲线C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8547f2b4e89b0ae1445bda02d46f0668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a789526b5dbf97449e2290e21a7aa48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.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/82b0aeee86644df4cd2f02f38e0535ec.png)
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2024-03-25更新
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1804次组卷
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8卷引用:广东省广州四中2023-2024学年高二下学期期中数学试题
广东省广州四中2023-2024学年高二下学期期中数学试题上海市七宝中学2024届高三上学期期中数学试题江苏省苏州市苏州实验中学2023一2024学年高二上学期12月质量检测数学试题(已下线)微考点6-1 圆锥曲线中的非对称韦达定理问题(三大题型)(已下线)大招18非对称处理山东省济宁市第一中学2024届高三下学期3月定时检测数学试题山东省济宁市第一中学2024届高三下学期4月质量检测数学试卷(已下线)大招4 圆锥曲线创新问题的速破策略
2 . 已知双曲线
的离心率
,抛物线
的准线经过其左焦点.
(1)求抛物线
的标准方程及其准线方程;
(2)若过抛物线
焦点
的直线
与该抛物线交于
、
两个不同的点,求证:以
为直径的圆与抛物线
的准线相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3680630fed86f1726f02d8a264ef0761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0276541c12707b24d2f06ea3d976cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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