名校
解题方法
1 . 设
为双曲线
:
上一动点,
,
为上、下焦点,
为原点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22df7f36d2d26a4624d47e65d675614.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/1dde8112e8eb968fd042418dd632759e.png)
A.若点![]() ![]() |
B.若过点![]() ![]() ![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() ![]() |
D.过![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-09-29更新
|
806次组卷
|
4卷引用:浙江省名校协作体2022-2023学年高二下学期联考数学试题
浙江省名校协作体2022-2023学年高二下学期联考数学试题浙江省宁波市鄞州中学2023-2024学年高二上学期期中考试数学试题(已下线)模块三 专题4 圆锥曲线中的最值和范围问题(高二人教A)(已下线)专题3.2 双曲线(5个考点十大题型)(3)
2 . 已知点
是双曲线
与椭圆
的公共点,直线
与双曲线
交于不同的两点
,
,设直线
与
的倾斜角分别为
,
,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/a8ccb6e8-8ffc-42f7-a3a8-3d79b2ebce40.png?resizew=212)
(1)求证:直线
恒过定点,并求出定点坐标;
(2)记(1)中直线
恒过定点为
,若直线
与椭圆
交于不同两点
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d52ad74a134ca8a65cb9ad8ef5cbd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40499eaaf1e6ac9d8da30ccbbcaf5aac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f478abeeb4da23121b652cf907972d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/a8ccb6e8-8ffc-42f7-a3a8-3d79b2ebce40.png?resizew=212)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)记(1)中直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/25a183c9577e8730b7962f75fc3f6e0c.png)
您最近一年使用:0次
解题方法
3 . 已知曲线
,焦点
,
,
,
,
是左支上任意一点(异于点
),且直线
与
的斜率之积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/dbd39062-145e-47ee-8380-9254811e5401.png?resizew=235)
(1)求曲线
的方程;
(2)直线
为过
点的切线,直线
与直线
关于直线
对称,直线
与
轴的交点
,过点
作直线
的平行线与曲线
交于
,
两点,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3030c1ec9b7040325865ed7e2ae4c6.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/bc269fc04b75a3b88715a30fe9c080fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d850f8e63fdf3861d2aa77cd5da2812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/dbd39062-145e-47ee-8380-9254811e5401.png?resizew=235)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0be8172856a4123ccf9c9e35b89f917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
您最近一年使用:0次
4 . 已知双曲线
,过该曲线上的点
作不平行于坐标轴的直线
交双曲线的右支于另一点
,作直线
交双曲线的渐近线于两点A,B(A在第一象限),其渐近线方程为
,且
,
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/584c79b3-4c22-4b33-9600-735558ad9b2a.png?resizew=157)
(1)求双曲线方程.
(2)证明:直线
过定点.
(3)当
的斜率为负数时,求四边形
的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac5225ff6aa3c06ff5c8437f88093f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176877187312e07c3a04c73718fa39a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/421e012e863cd15eea1a174cd0679c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc44dadecd4e362fcfd50fcf789fe696.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/584c79b3-4c22-4b33-9600-735558ad9b2a.png?resizew=157)
(1)求双曲线方程.
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712d9d9e29645c1df6ae23125b4aa1cc.png)
您最近一年使用:0次
名校
解题方法
5 . 已知双曲线
的中心为坐标原点,对称轴为坐标轴,且过点
两点.
(1)若双曲线
的右支上的三个不同的点
关于
轴的对称点分别为
双曲线的左右焦点,试求
的值;
(2)设过点
的直线
交曲线
于
两点,过
作
轴的垂线与线段
交于点
,点
满足
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c253d53593f994122fcb5f3301e8aad4.png)
(1)若双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7807638578edd712265463a7a5eab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bda58f9753ee60b71b447a005a03f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90adf36c39064c6eec958cf7edae58dc.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f4b2e47f04efd6b39e2ec12b3ca7de.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49838a24c28cdc18dab9990a0a72e286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
您最近一年使用:0次
2022-11-23更新
|
367次组卷
|
2卷引用:浙江省衢州市普通高中2022-2023学年高三上学期素养测评数学试题
名校
解题方法
6 . 已知等轴双曲线
过定点
,直线
与双曲线
交于
两点,记
,且
.
(1)求等轴双曲线
的标准方程;
(2)证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79238e14cbbc951421c74471f9df8692.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c21fdf33b6370afbdd5e1b3fee34cc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445bf1af0740c861e152d076f20f1ab2.png)
(1)求等轴双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次