1 . 设A,B是双曲线H:
上的两点.直线l与双曲线H的交点为P,Q两点.
(1)若双曲线H的离心率是
,且点
在双曲线H上,求双曲线H的方程;
(2)设A、B分别是双曲线H:
的左、右顶点,直线l平行于y轴.求直线AP与BQ斜率的乘积,并求直线AP与BQ的交点M的轨迹方程;
(3)设双曲线H:
,其中
,
,点M是抛物线C:
上不同于点A、B的动点,且直线MA与双曲线H相交于另一点P,直线MB与双曲线H相交于另一点Q,问:直线PQ是否恒过某一定点?若是,求该定点的坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
(1)若双曲线H的离心率是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc709512ea41db03985e5546d0bd86c.png)
(2)设A、B分别是双曲线H:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
(3)设双曲线H:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c9e49809ed819892738b698c73e7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f81f26377b516bb1184288681cd4dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
您最近一年使用:0次
名校
解题方法
2 . 已知双曲线
的左、右顶点分别为
,
,渐近线方程为
,过左焦点
的直线
与
交于
,
两点.
(1)设直线
,
的斜率分别为
,
,求
的值;
(2)若直线
与直线
的交点为
,试问双曲线
上是否存在定点
,使得
的面积为定值?若存在,求出定点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.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/9b6bb019e2d7c6d17d15ec4d9043f5e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030700126fb012f13935f57780b96677.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.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/b4757181824e15e0f21e5bdd55448783.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e29303195c563855aee4c14cbcb9bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2024-06-14更新
|
381次组卷
|
3卷引用:江西省上饶市稳派上进六校联考2024届高三5月第二次联合考试数学试题
名校
3 . 已知椭圆
的左右顶点分别为
,点
是椭圆
上任意一点,点
和
关于
轴对称,设直线
和
交点为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求点
的轨迹
的方程;
(2)若
为曲线
的右焦点,过
的直线与
交
,
两点,
在第二象限,
(i)以
为直径的圆是否经过点
,若是,请说明理由;
(ii)设
为直径的圆与曲线
在第一象限交点为
,证明点
是
的内心.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14bc72784bcebeed033bf402f63c882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663368000ac90f582d12675aa2d1e832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd4face613deea6dde85915615d6f726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(i)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68fd4e950b44bd49949ba776c5ef8a6.png)
您最近一年使用:0次
2024高三·全国·专题练习
4 . 已知双曲线
:
和椭圆
:
.过点
的动直线
交
于A,B两点,过点Р的动直线
交
于M,N两点,若四条直线
的斜率之和为定值,则定点Q为_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b7c3cd7bea116f532f66fba44662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a714873b3c65e7c3a6ad802fa7095e.png)
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2024·全国·模拟预测
解题方法
5 . 已知双曲线
的左、右焦点分别为
,
,点
是
上一点.若
为
的内心,且
.
(1)求
的方程;
(2)点A是
在第一象限的渐近线上的一点,且
轴,点
是
右支上的一动点,
在点
处的切线
与直线
相交于点
,与直线
相交于点
.证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1723a5c1980f59baa9a949624d049332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f9d178764408489b0b336ea0ee42a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ddd3b35e93494d5bddf56f3b3007f5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)点A是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5dc06fe67c281c3ad3d19d6d8c98a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2752e086b85f9fbb95010bf771072af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.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/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a873e20e420dc0904e8cc90eb230fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f93c3a552853bd28fdffe4de661d256.png)
您最近一年使用:0次
解题方法
6 . 已知双曲线
,上顶点为
,直线
与双曲线
的两支分别交于
两点(
在第一象限),与
轴交于点
.设直线
的倾斜角分别为
.
(1)若
,
(i)若
,求
;
(ii)求证:
为定值;
(2)若
,直线
与
轴交于点
,求
与
的外接圆半径之比的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7bcb34ed3bf1981b04d07b53030264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342ba1917a6b854ad111a3e6f5514934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d5467e6dd66a263e3b8607385c2acf.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71885f023172807ad43f2c9a670aa960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093c05ac99b784f79ab03edb81bdc8c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554bc87180cd813a4c5d4eb88996d089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847a4906dd3bb720f3c340cea2d297dc.png)
您最近一年使用:0次
7 . 已知曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
,
是坐标原点, 过点
的直线
与曲线
交于
,
两点.
(1)当
与
轴垂直时,求
的面积;
(2)过圆
上任意一点
作直线
,
,分别与曲线
切于
,
两 点,求证:
;
的直线
与双曲线
交于
,
两点(
,
不与
轴重合).记直线
的斜率为
,直线
斜率为
, 当
时,求证:
与
都是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80b861ba40387cb2bcd04945f5a371a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5226a2e1ee83a869b1133a234e9f3108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
(2)过圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be68dfb4d8b5f3adfc250b7d23e64165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.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/ada25f76504c3fd1226da43c94cb4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944e8452701ba3a0bf9d8561f7a4cad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b7c3cd7bea116f532f66fba44662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b647e083b52664749a2c07a13b6089c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284185654ca00ac9df0155d4c519a063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d303eb7923a91dcecc2d9bc1133d5c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38d23c520f89002afb0338bcb7b62c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22871505498b73670d0ee432ba402631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2297d08e5496a1af3f9ed1a1bbaea06.png)
您最近一年使用:0次
8 . 已知双曲线
与曲线
有4个交点
(按逆时针排列)
(1)当
时,判断四边形
的形状;
(2)设
为坐标原点,证明:
为定值;
(3)求四边形
面积的最大值.
附:若方程
有4个实根
,
,
,
,则
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da601fb83011f1f6bf8a60b1d3a6a6cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731809d4e06dfcdb73811b99da26f00e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c43f86ecb6bb6dfb3331b26d957d59d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5325019987094e4b36570319fdf1a9.png)
(3)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
附:若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdf06ae0fe7b5de03c3d1d68270fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec413484532aa969f9cfa4b90adc004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b271fb5eff2dcde48ea2a9a7c580f621.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
9 . 已知双曲线
的两条渐近线方程为
分别为双曲线
的顶点,且
.
(1)求双曲线
的方程.
(2)已知
为坐标原点,直线
与双曲线
交于
两点,且
,求
的值.
(3)设动点
,直线
与双曲线
分别交于
两点.求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c4088276acdbede4781b2ebc466366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8cdf634b9e77475e97ffa8f3043112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231896d2386c924306fce5ccf9f9e8a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85de1d945232cdeeb6bf999241441630.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b986e3613290b456532843d5ad4c6e67.png)
(3)设动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fb95c0dbba2ce77a7dcc42fa06e058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fb7ec4aa413693f4ecae59fe0e2084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
10 . 如图,已知双曲线
的离心率为2,点
在
上,
为双曲线的左、右顶点,
为
右支上的动点,直线
和直线
交于点
,直线
交
的右支于点
.
的方程;
(2)探究直线
是否过定点,若过定点,求出该定点坐标;否则,请说明理由;
(3)设
分别为
和
的外接圆面积,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3fc6891aacb2287358410e0e649cd1.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)探究直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8428037a379bcd01cfffd5aa9434dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142b9d242ef0c6b807d1257f2638b37b.png)
您最近一年使用:0次
2024-04-10更新
|
757次组卷
|
3卷引用:安徽省池州市第一中学2024届高三第一次模拟联合检测数学试题