名校
解题方法
1 . 直线
过双曲线
的一个焦点,且直线l与双曲线C的一条渐近线垂直.
(1)求双曲线C的方程;
(2)过点
作一条斜率为k的直线
,若直线
上存在点P,使得过点P总能作C的两条切线互相垂直,求直线k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ade7a00bc38f22c547f5d96e2e8252b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
(1)求双曲线C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d2ab6fcfa7fa478a65bdee609149d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
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名校
解题方法
2 . 已知双曲线
:
的离心率为
,直线
:
与双曲线C仅有一个公共点.
(1)求双曲线
的方程
(2)设双曲线
的左顶点为
,直线
平行于
,且交双曲线C于M,N两点,求证:
的垂心在双曲线C上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59f8afa4c99e0fc6210cf98646f0ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38646f7466d36f4bcce1b87d6e4b23.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
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2023-03-24更新
|
2597次组卷
|
8卷引用:福建省莆田市第六中学2024届高三上学期1月质检模拟数学试题
名校
解题方法
3 . 已知双曲线
的左、右焦点分别为
,
,左顶点为
,点M为双曲线上一动点,且
的最小值为18,O为坐标原点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/8e810855-8c23-439b-b5db-521a07fcd763.png?resizew=245)
(1)求双曲线C的标准方程;
(2)如图,已知直线
与x轴的正半轴交于点T,过点T的直线交双曲线C右支于点B,D,直线AB,AD分别交直线l于点P,Q,若O,A,P,Q四点共圆,求实数m的值.
![](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/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8119c3efb56372a1b4e6d7951b027de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/8e810855-8c23-439b-b5db-521a07fcd763.png?resizew=245)
(1)求双曲线C的标准方程;
(2)如图,已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be03641c9e23456c63a8eb57a3540f62.png)
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2023-03-13更新
|
2029次组卷
|
4卷引用:重庆市南开中学校2023届高三第七次质量检测数学试题
重庆市南开中学校2023届高三第七次质量检测数学试题四川省阆中中学校2023届高三下学期3月月考数学理科试题重庆市2023届高三第七次质量检测数学试题(已下线)第五篇 向量与几何 专题10 圆锥曲线中的四点共圆问题 微点2 圆锥曲线中的四点共圆问题(二)
4 . 已知双曲线
的实轴长为
,右焦点F到双曲线C的渐近线距离为1.
(1)求双曲线C的方程;
(2)点P在第一象限,
在直线
上,点
均在双曲线C上,且
轴,M在直线
上,
三点共线.从下面①②中选取一个作为条件,证明另外一个成立:①Q是
的中点;②直线
过定点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求双曲线C的方程;
(2)点P在第一象限,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d585d2d6643471640905d234d9538c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01225eca2322a6136314dedadcafa994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ec40adf62bc48e014d76647f1eabce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2834be81b26fcc80d4f4ae04845b612b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3627350f7d2ef1a7fb62343407719d4.png)
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5 . .已知双曲线
的虚轴长为
,右焦点为
,点
、
分别为双曲线
的左、右顶点,过点
的直线
交双曲线的右支于
、
两点,设直线
、
的斜率分别为
、
,且
.
(1)求双曲线
的方程:
(2)当点
在第一象限时,且
时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/c5db41a1f31d6baee7c69990811edb9f.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.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/03b8bfb1960c394ccfb7bb12de1c1b2b.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec79607071014df4522d49f117583c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
解题方法
6 . 定义两个点集S、T之间的距离集为
,其中
表示两点P、Q之间的距离,已知k、
,
,
,若
,则t的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc583b7bb3ab41850a8a2447a7abaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7033cdfb9fb5770ca833f2c83ecb3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450f84739e8a2d21b374ccedc8972605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56d22586bc5fb71fe1b442ee7580268.png)
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2023-03-02更新
|
2204次组卷
|
9卷引用:上海市嘉定区2023届高三下学期2月调研数学试题
7 . 已知双曲线
的离心率为2,右焦点F到渐近线的距离为
,过右焦点F作斜率为正的直线l交双曲线的右支于A,B两点,交两条渐近线于C,D两点,点A,C在第一象限,O为坐标原点.
(1)求双曲线E的方程;
(2)设
,
,
的面积分别是
,
,
,若不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c4088276acdbede4781b2ebc466366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求双曲线E的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173bc7a36757d77f01213411edd25241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7bd8bfbd43d0cf1604b8d7e0023f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42657818f3305f210260507c5cb9753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be1ecc98d8990cac06ec348c557de09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a711bf44ed64556c72fbb0e7f42c27f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8dc0adb9debd94f431486545c4825e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2023-02-25更新
|
1116次组卷
|
3卷引用:江西省贵溪市实验中学2023届高三第四次月考数学(文)试题
名校
解题方法
8 . 已知点M为圆
上的动点,点
,延长
至N,使得
,线段
的垂直平分线交直线
于点P,记P的轨迹为
.
(1)求
的方程;
(2)直线l与
交于A,B两点,且
,求
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ba951ce58ff7fb59c57e2d349fdc4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8ad9e94d07405a6be585f81a0d623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cae6a406507d1c4ded678359ca9e38f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7272356beb98a7953a49651324cb6455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbdbe9a17a23c44cec8c7475c4dc1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)直线l与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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2023-02-19更新
|
716次组卷
|
4卷引用:福建省泉州市2023届高三毕业班质量监测(二)数学试题
名校
解题方法
9 . 已知双曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98039a3c75554c5eae14dbe8caba181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
的右焦点为F,双曲线C上一点
关于原点的对称点为
,满足
.
(1)求
的方程;
(2)直线
与坐标轴不垂直,且不过点
及点
,设
与
交于
、
两点,点
关于原点的对称点为
,若
,证明:直线
的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98039a3c75554c5eae14dbe8caba181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d3f9d8344e1c727fbbed5421daaa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae104d6d67d114b588a5680b124b0e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ab65560eb03ee1466d4356ba572a5b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](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/acc290b44635265137fdf13146b6a6d9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-02-07更新
|
1640次组卷
|
3卷引用:湖南省长沙市长郡中学2023届高三下学期月考(六)数学试题
22-23高三上·江苏南通·期末
名校
解题方法
10 . 在平面直角坐标系xOy中,已知圆E:
和定点
,P为圆E上的动点,线段PF的垂直平分线与直线PE交于点Q,设动点Q的轨迹为曲线C.
(1)求曲线C的方程;
(2)设曲线C与x轴正半轴交于点A,过点
的直线l与曲线C交于点M,N(异于点A),直线MA,NA与直线
分别交于点G,H.若点F,A,G,H四点共圆,求实数t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f269f3d5e4148989d8897efa29cc60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
(1)求曲线C的方程;
(2)设曲线C与x轴正半轴交于点A,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17472f36adda39804d085fb0ed031f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
您最近一年使用:0次