解题方法
1 . 双曲线
的一个焦点为
,中心为原点,过
的直线
与C交于
,
两点,若
的中点为
,则此双曲线的渐近线方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2254f7a85430f9c0b1adf193318dbf6.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)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b5c3d9d91d6109bf2fb0c2eb7daf7b.png)
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解题方法
2 . 给出问题:已知双曲线方程为
,问以定点
为中点的弦存在吗?若存在,求出其所在直线的方程;若不存在,请说明理由.
某学生的解答如下:过点
与
轴垂直的直线与双曲线只有唯一的公共点
,显然不符题意,所以可设所求直线的斜率为
,则直线方程为
,即
,将它代入得
,
,设直线与双曲线相交于
,则
,若
为线段
的中点,则
,即
,解得
.所以满足条件的直线存在,方程为
.
该学生的解答是否正确?并说明理由_______________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fd2d54fe9e90077e7d27edc009edce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d3bfa155ad67018da4d65815c5e5b8.png)
某学生的解答如下:过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d3bfa155ad67018da4d65815c5e5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b695053527fb771a3d4bcf6eb113c4ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47460bfa9afca6625f8f9696901b2392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fd2d54fe9e90077e7d27edc009edce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/361bbc3bca75423f6a333640122bf79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7d5b7a335fb30a034976287aee9e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dbfb9fea4b681196b2c7df4c4f3a380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d3bfa155ad67018da4d65815c5e5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419504736c4934f6e0df4114c3743944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c2eae7b94a94e684333bcee5fe5f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e788c32187ae2cc97aaa24da1d40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc568fbc1480ba87cfdc2b6b3c71200.png)
该学生的解答是否正确?并说明理由
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解题方法
3 . 已知双曲线
上有三个点
,
,
且
,
,
的中点分别为
,
,
,用字母
表示斜率,若
(点
为坐标原点,且
,
,
均不为零),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b7a1534e025a175ed9ea11ab58201b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acac8b38a645b428474006d802af038.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1aaaec553e89fad992feb13e714ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b7a1534e025a175ed9ea11ab58201b.png)
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2020-12-13更新
|
210次组卷
|
4卷引用:河南省周口市商丘市大联考2020-2021学年高三阶段性测试(三)理科数学试题
名校
解题方法
4 . 双曲线
的右焦点分别为F,圆M的方程为
.若直线l与圆M相切于点
,与双曲线C交于A,B两点,点P恰好为AB的中点,则双曲线C的方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a308b980f486306256e425a1a1018b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89ddbe4682391f62c908f0f774d32a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9311899128cc61536d31701822880ee5.png)
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2020-12-12更新
|
610次组卷
|
7卷引用:陕西省西安市2019-2020学年高二上学期期末数学(文)试题
陕西省西安市2019-2020学年高二上学期期末数学(文)试题四川省成都市树德中学2019-2020学年高二下学期定时检测(线上开学考试)数学试题(已下线)2.3.1+双曲线及其标准方程(重点练)-2020-2021学年高二数学(理)十分钟同步课堂专练(人教A版选修2-1)(已下线)2.2.1+双曲线及其标准方程(重点练)-2020-2021学年高二数学(文)十分钟同步课堂专练(人教A版选修1-1)(已下线)3.2.1 双曲线及其标准方程(重点练)-2020-2021学年高二数学十分钟同步课堂专练(人教A版选择性必修第一册)四川省成都市树德中学2019-2020学年高二下学期开学考试数学试题(已下线)3.2.2 双曲线的简单几何性质(精练)-2021-2022学年高二数学一隅三反系列(人教A版2019选择性必修第一册)
名校
解题方法
5 . 已知双曲线方程是
,过定点
作直线交双曲线于
两点,并使
为
的中点,则此直线方程是__________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed5a489515879d019a8a6ec6b84361b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4754fbe523ca63eba3810a3f88f37df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
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2020-11-22更新
|
221次组卷
|
2卷引用:黑龙江省哈尔滨市第六中学2020-2021学年高二上学期期中考试数学(文)试题
解题方法
6 . 已知双曲线
和点
,直线
经过点
且与双曲线相交于
、
两点,当
恰好为线段
的中点时,
的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b7c3cd7bea116f532f66fba44662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e280d0441a31fdbef3ce192d8d8f8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
7 . 经过点
作直线
交双曲线
于
两点,且
为
的中点,则直线
的方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844363690c82dfa4eba1a47915f4120b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d34cf4ed961f4052ed35c7475c7d32e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb398137779190b35492d9f06d5fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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8 . 已知曲线
:
,点
,
在曲线
上,且以
为直径的圆的方程是
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf7def0c6cf92746f3081692303da21.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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2020高三·全国·专题练习
解题方法
9 . 点
是曲线C:
的弦
的中点.则直线
的方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d783f0ae55e385002bd6df9a0ac21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b7c3cd7bea116f532f66fba44662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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