名校
1 . 已知点
为双曲线
的左右焦点,过
作垂直于
轴的直线,在
轴上方交双曲线于点
,且
的面积为
.圆
的方程是
.
(1)求双曲线的方程;
(2)过双曲线上任意一点
作该双曲线两条渐近线的垂线,垂足分别为
,求
的值;
(3)过圆
上任意一点
作圆
的切线
交双曲线
于
两点,
中点为
,若
恒成立,试确定圆
半径
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c652ef292861a171019076dc7d5df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.png)
(1)求双曲线的方程;
(2)过双曲线上任意一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594fa9a4bce1ed5fd27e4cb55d63cf0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ce7e97e482605c1965cbfcf895e340.png)
(3)过圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2260415102415b12efe70f11719d73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
2023-02-08更新
|
685次组卷
|
4卷引用:上海市交通大学附属中学2022届高三上学期期末数学试题
上海市交通大学附属中学2022届高三上学期期末数学试题(已下线)专题10 圆锥曲线综合大题10种题型归类-【寒假分层作业】2024年高二数学寒假培优练(人教A版2019选择性必修第一册)上海市奉贤区奉贤中学2024届高三下学期开学考试数学试题(已下线)专题7-4圆锥曲线五个方程型大题归类-2
名校
解题方法
2 . 已知双曲线
的一条渐近线方程为
,点
在双曲线
上.
(1)求双曲线
的标准方程;
(2)过定点
的动直线
与双曲线
的左、右两支分别交于
两点,与其两条渐近线分别交于
(点
在点
的左边)两点,证明:线段
与线段
的长度始终相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c204834608f1a8fba15747210dd7c5af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e0e6f0e61d018db53aba289fc8be45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
您最近一年使用:0次
2022-12-16更新
|
378次组卷
|
4卷引用:吉林省四平市第一高级中学2021-2022学年高二上学期第三次月考数学试题
2021高二·全国·专题练习
解题方法
3 . 已知双曲线
的两个焦点为
、
,一条渐近线方程为
,且双曲线
经过点
,
.
(1)求双曲线C的方程;
(2)设点
在直线
,
,且
为常数)上,过点
作双曲线
的两条切线
、
,切点为
、
,求证:直线
过某一个定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db0cc24753f6ea44c19c3cc49e26024.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/d7d4f20f4d98141613ff5dd7c37b55c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af649e5ec3b6943e4d4c737a2a530808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf8a317ccc87a1bf8e17852fddbe29.png)
(1)求双曲线C的方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75067666bd2907d4e8a8ffc8b90b86eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9e329f2730b2be926b121f1ae04c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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)
您最近一年使用:0次
4 . 已知双曲线Γ:
经过点
,且其中一焦点
到一条渐近线的距离为1.
(1)求双曲线Γ的方程;
(2)过点P作两条相互垂直的直线PA,PB分别交双曲线Γ于A,B两点,求点P到直线AB距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8737f509bc3af89d30f54b4112086a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求双曲线Γ的方程;
(2)过点P作两条相互垂直的直线PA,PB分别交双曲线Γ于A,B两点,求点P到直线AB距离的最大值.
您最近一年使用:0次
2022-11-23更新
|
518次组卷
|
6卷引用:专题01 《圆锥曲线与方程》中的典型题(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
(已下线)专题01 《圆锥曲线与方程》中的典型题(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) 内蒙古鄂尔多斯市第一中学2018-2019学年高二下学期第一次月考数学(理)试题(已下线)易错点13 圆锥曲线及直线与圆锥曲线位置关系-2(已下线)江苏省盐城市、南京市2022届高三上学期1月第一次模拟考试数学试题变式题17-22浙江省绍兴市第一中学2022-2023学年高三上学期10月月考数学试题(已下线)专题3.10 圆锥曲线的方程全章八类必考压轴题-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)
2021·全国·模拟预测
解题方法
5 . 已知抛物线
的焦点为
,双曲线
的斜率大于
的渐近线为
,过点
作直线
,交抛物线
于
、
两点,且
.
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882960865665024/2883214394482688/STEM/d58a9cdb98ef44599d57a448bee8961f.png?resizew=273)
(1)求抛物线
的方程;
(2)若直线
,且与抛物线
相切于点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d624a18acd4fccfedaf984862adc004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9834888367862d17f5118d95ba3108b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24caeb80a748bcbc9dc33cd430a5aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/82796f5bb05438453a1e06a4fa83d6a1.png)
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882960865665024/2883214394482688/STEM/d58a9cdb98ef44599d57a448bee8961f.png?resizew=273)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354bb54738c66f16e4df22a531556feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc157c66eef6affd86e48432176c4240.png)
您最近一年使用:0次
2021·全国·模拟预测
解题方法
6 . 双曲线C:
(
,
)的一条渐近线l的倾斜角为
,过左、右焦点
,
分别作l的垂线,两垂足间的距离为
.
(1)求双曲线C的方程;
(2)过点P(1,0)且斜率不为0的直线
与双曲线C交于M,N两点,记N关于x轴的对称点为Q,证明直线MQ过x轴上的定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.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/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求双曲线C的方程;
(2)过点P(1,0)且斜率不为0的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
名校
7 . 在平面直角坐标系中,
为坐标原点,已知双曲线
:
的右焦点
到双曲线
的一条渐近线
的距离为
.
![](https://img.xkw.com/dksih/QBM/2021/11/24/2858221922107392/2859222073040896/STEM/9d2b0280-6c32-490c-b1b7-8582876b3df2.png)
(1)求双曲线
的方程;
(2)如图,过圆
:
上一点
作圆
的切线
与双曲线
的左右两支分别交于
,
两点,以
为直径的圆经过双曲线
的右顶点
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/2021/11/24/2858221922107392/2859222073040896/STEM/9d2b0280-6c32-490c-b1b7-8582876b3df2.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)如图,过圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2021-11-26更新
|
1151次组卷
|
5卷引用:重庆市缙云教育联盟2021-2022学年高二上学期11月质量检测数学试题
重庆市缙云教育联盟2021-2022学年高二上学期11月质量检测数学试题重庆市巴蜀中学2022届高三上学期高考适应性月考(四)数学试题(已下线)专题41 圆锥曲线中必考的双曲线问题-备战2022年高考数学一轮复习一网打尽之重点难点突破河北省2023届高三模拟演练(1)数学试题重庆市育才中学校2023届高三4月诊断模拟数学试题
名校
解题方法
8 . 在平面直角坐标系
中,已知双曲线
.
(1)写出过双曲线C的左顶点且与双曲线两条渐近线平行的直线方程;
(2)设F是C的左焦点,M是C右支上一点.若
,求过M点的坐标;
(3)设斜率为
的直线
交C于P、Q两点,若l与圆
相切,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d11a263b2cb524d5dd680129f5a152.png)
(1)写出过双曲线C的左顶点且与双曲线两条渐近线平行的直线方程;
(2)设F是C的左焦点,M是C右支上一点.若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8ff5be2ec9739899b143ed1208ff9e.png)
(3)设斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8203f0d70f1b4c0921743e323a946c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
您最近一年使用:0次
9 . 在平面直角坐标系
中,对于直线
和点
,
,记
,若
,则称点
,
被直线l分离,若曲线c与直线l没有公共点,且曲线c上存在点
,
被直线l分隔,则称直线l为曲线c的一条分隔线.
(1)求证:点
,
被直线
分隔;
(2)若直线
是曲线
的分隔线,求实数k的取值范围;
(3)动点M到点
的距离与到y轴的距离之积为1,设点M的轨迹为曲线E,求证:通过原点的直线中,有且仅有一条直线是E的分隔线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fa0e0526598c4140789f6328daac9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b225d772013d021cf1bfe7b9421fa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b7e35faab6d74fa0c36599c39d1698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b291c8f35ccdab81c474f286f6dc7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5e2c8b545bc2a67ee4b024ab219b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42f05b013e4b7166cbc87c5a83d6a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348aca26e61218d251581e21c1129a8a.png)
(3)动点M到点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75ebcf0d951f833ca90e040f3cd4db6.png)
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解题方法
10 . 已知双曲线C的焦点到其渐近线
的距离为2.
(1)求双曲线C的标准方程;
(2)设双曲线C的焦点在x轴上,过点
的直线l交C双曲线的左右两支分别于A,B,交渐近线分别于M,N,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10273b05ad8210d8db07639c4d149fd.png)
(1)求双曲线C的标准方程;
(2)设双曲线C的焦点在x轴上,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29819c98ebd087116d5e579f4f088fe8.png)
您最近一年使用:0次