1 . 已知椭圆
过点
,且离心率为
.
(1)求椭圆的标准方程;
(2)已知圆
.过点
作直线
和
,且两直线的斜率之积等于
与圆
相切于点
与椭圆相交于不同的两点
.
①求
的取值范围;
②求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d7d081740b8e2c85df850572b9e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求椭圆的标准方程;
(2)已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9e97e93b5c8704137de074b3890cb.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/e51b55e34efa5a5b8da548bcb4427572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec36f7c1eb7d1367e91127bcfb78e504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
2 . 已知数列
满足:
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e98bbb6af2653589c3027021981e703.png)
A.![]() |
B.![]() |
C.![]() |
D.当![]() ![]() |
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解题方法
3 . 过双曲线
的左焦点
作
的一条渐近线的垂线,垂足为
,这条垂线与另一条渐近线在第一象限内交于点
为坐标原点,若
,则
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/7f4411b37e8ed03b1841906af3bf912f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa55fad4e4efb7b8c5fe10f7edeb56e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
解题方法
4 . 已知双曲线
:
的左、右顶点分别为
,
,且顶点到渐近线的距离为
,点
是双曲线
右支上一动点(不与
重合),且满足
,
的斜率之积为
.
(1)求双曲线
的方程.
(2)过点
的直线
与双曲线
交于
轴上方的
,
两点,若
是线段
的中点,
是线段
上一点,且
,
为坐标原点,试判断直线
,
的斜率之积是否为定值.若为定值,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.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/cd3b9e816b14051f785aa5aae72b8eed.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/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23728b4c0467a27d90f71b424f6a946.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/81dea63b8ce3e51adf66cf7b9982a248.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05793d7de026a194dac40a666e53d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
您最近一年使用:0次
2023-06-20更新
|
368次组卷
|
4卷引用:贵州省毕节市织金县第九中学2022-2023学年高二下学期期中数学试题
名校
解题方法
5 . 如图,已知双曲线
的右焦点为F,过点F的直线与双曲线的两条渐近线相交于M,N两点.若
,则双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67533988d89e1bbc0d4f733b3f4f6eb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/13/73339a85-6158-410b-b30d-61f068abdde3.png?resizew=165)
A.![]() | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
2023-06-08更新
|
1240次组卷
|
4卷引用:贵州省威宁县第八中学2022-2023学年高二下学期第二次月考数学试题
解题方法
6 . 设
,若关于x的不等式
在
上恒成立,则
的值可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7848e45c087ab7fb8e60657ba898cf5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21645b61263c54dc9943dbf963e2673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f25ca6ba3b1abc3443093f32360d1b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
7 . 设有一组圆
:
,下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94555857a26590865f337f8c4a93c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527eed7d9e9c352f55561a39d09579.png)
A.不论![]() ![]() |
B.若点![]() ![]() ![]() |
C.若圆![]() ![]() ![]() |
D.若圆![]() ![]() |
您最近一年使用:0次
2023-04-26更新
|
583次组卷
|
2卷引用:贵州省毕节市金沙县2022-2023学年高二上学期12月月考数学试题
名校
解题方法
8 . 已知椭圆
:
的左、右焦点分别为
,
,过椭圆
上一点
和原点
作直线
交圆
:
于
,
两点,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28a31a11044d169f3d6a892913b9dde.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945066b2767be49535b0f9529649b834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.椭圆![]() ![]() |
B.若![]() ![]() ![]() |
C.![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2023-04-26更新
|
659次组卷
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4卷引用:贵州省毕节市金沙县2022-2023学年高二上学期12月月考数学试题
贵州省毕节市金沙县2022-2023学年高二上学期12月月考数学试题江西省多所重点校2022-2023学年高二上学期12月统一调研数学试题黑龙江省大庆市大庆中学2023届高三三模数学试题(已下线)江苏省南京市六校联合体2023-2024学年高三上学期11月期中数学试题变式题11-14
解题方法
9 . 已知双曲线
:
的左、右焦点分别为
,
,
的右顶点
在圆
上,且
.
(1)求
的方程;
(2)若
,
是双曲线
上位于
轴上方的两点,且
,
与
交于点
,证明:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114cdce00937ef85c0cd95538cea69e4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d4f42c799e2845340f8726ed39a2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe1cad1ce47339827ac5047af4647d.png)
您最近一年使用:0次
2023-04-26更新
|
202次组卷
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2卷引用:贵州省毕节市金沙县2022-2023学年高二上学期12月月考数学试题
解题方法
10 . 已知函数
,若关于
的不等式
(
是自然对数的底数)在
上恒成立,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46300c1300c051f15f78fe7287f8056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f1467881d86dd83e90db9d24b43428.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2022-07-20更新
|
946次组卷
|
4卷引用:贵州省毕节市2021-2022学年高二下学期联合考试数学(理)试题
贵州省毕节市2021-2022学年高二下学期联合考试数学(理)试题内蒙古自治区通辽市霍林郭勒市2021-2022学年高二下学期期末数学理科试题(已下线)专题3-1 切线、公切线及切线法应用 - 2(已下线)专题05 导数在切线中的相关运用-2