1 . 已知点,动点
在直线
:
上,过点
且垂直于
轴的直线与线段
的垂直平分线交于点
,记点
的轨迹为曲线
.
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/299b9274e61eafb5bb2d07f8d5a70bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74625390340982140e449e07663579a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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2024-01-13更新
|
595次组卷
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8卷引用:湖北省武汉市第六中学2022-2023学年高二下学期第四次月考数学试题
湖北省武汉市第六中学2022-2023学年高二下学期第四次月考数学试题安徽省江淮十校2023届高三三模数学试题重庆市南开中学校2023届高三第九次质量检测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安徽省淮北市树人高级中学2023-2024学年高三上学期开学检测数学试题(已下线)专题15 圆锥曲线综合广东省珠海市第一中学2024届高三上学期大湾区期末数学预测卷(五)(已下线)重难点14 圆锥曲线必考压轴解答题全归类【十一大题型】(举一反三)(新高考专用)-1
名校
解题方法
2 . 已知函数
.
(1)当
时,求
在
的切线方程;
(2)若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e70f2cbcf8bcb60c75e1779fc2b7d6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6711f624336a86026873ac5616ac72c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
与
有两个不同的交点,交点坐标分别为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590a7d430703d2d41a0171ff6a97dac5.png)
,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7029bd8089800bab0111238b4ed8b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693f047cefe8477d055076b0fb25a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590a7d430703d2d41a0171ff6a97dac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af029e933ded38d74c2a9d283e3b92d3.png)
A.![]() ![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2024-01-11更新
|
343次组卷
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3卷引用:湖北省武汉市东湖中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
4 . 如图,已知椭圆
,其焦距为4,过椭圆长轴上一动点
作直线交椭圆于
、
,直线
、
交于点
,已知
,则椭圆的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715abe79425e4e4f2a35fdd745ba653b.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468fc3e395fa3b681c3da37edbe229a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25ec7f5d958d54f9642eecec56e7540.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/f78746a7-c640-4a95-b14e-790feb628e1b.png?resizew=189)
您最近一年使用:0次
2024-01-11更新
|
287次组卷
|
2卷引用:湖北省武汉市东湖中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
5 . 如图,已知椭圆
,长轴长为6,离心率为
,过椭圆右焦点
作斜率不为0的直线交椭圆于
、
,过
作
垂直于直线
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/1285412a-c035-447c-87e4-817d66631e39.png?resizew=186)
(1)求椭圆的标准方程;
(2)证明:直线
过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090c0ba4cadbd85bf1f04f0d962eb16a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15febfda66e733f14aa7115ed4343a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/1285412a-c035-447c-87e4-817d66631e39.png?resizew=186)
(1)求椭圆的标准方程;
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3d566704b44ea4ef1f99c37bd46902.png)
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2024-01-11更新
|
518次组卷
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2卷引用:湖北省武汉市东湖中学2023-2024学年高二上学期期中考试数学试题
6 . 已知函数
,若方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
有三个不同的零点
,
,
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/444f7f1f30e332b41c0aa3af87d46fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8d1a34435611f6a59eac3dbfeb6e17.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/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
A.实数![]() ![]() | B.函数![]() ![]() |
C.![]() ![]() | D.函数![]() |
您最近一年使用:0次
名校
解题方法
7 . 在数学中,布劳威尔不动点定理是拓扑学里一个非常重要的不动点定理,它可应用到有限维空间,并构成一般不动点定理的基石,布劳威尔不动点定理得名于荷兰数学家鲁伊兹·布劳威尔,简单的讲就是对于满足一定条件的连续函数
,存在一个实数
,使得
,那么我们称该函数为“不动点”函数,
为函数的不动点.设函数
,
.若
在区间
上存在不动点,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4eb0f8fd7662afc6fab4f38e8c229a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed18bd80c6c4142f68e89f4ad44570b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-01-08更新
|
519次组卷
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5卷引用:湖北省部分学校2024届高三上学期12月联考数学试题
湖北省部分学校2024届高三上学期12月联考数学试题河北省保定市部分高中2024届高三上学期12月联考数学试题河北省保定市部分高中2024届高三上学期12月期中联考数学试题(已下线)模块五 期末重组篇 专题3 高三期末(已下线)模块三 专题3 题型突破篇 小题满分挑战练(3)
名校
解题方法
8 . 已知
是抛物线
的焦点,过点
作两条互相垂直的直线
、
,
与
相交于
,
两点,
与
相交于
,
两点,
为
,
中点,
为
,
中点,直线
为抛物线
的准线,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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)
A.![]() | B.以![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
2024-01-08更新
|
624次组卷
|
3卷引用:湖北省武汉市第三中学2023-2024学年高二上学期12月月考数学试题
解题方法
9 . 已知函数
.
(1)判断函数
的奇偶性;
(2)判断函数
的单调性并证明;
(3)若
对任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362bfce584209628bc4ad3f23e3d7b11.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892e23f6d6a845ac8ee4c9f84fe66ed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-01-05更新
|
711次组卷
|
3卷引用:湖北省咸宁市崇阳县第二高级中学2023-2024学年高一上学期数学模拟考试试题(一)
湖北省咸宁市崇阳县第二高级中学2023-2024学年高一上学期数学模拟考试试题(一)(已下线)高一上学期期末数学考试模拟卷-【题型分类归纳】(人教A版2019必修第一册)云南省祥华教育集团2023-2024学年高一下学期5月联考数学试题
10 . 已知椭圆
的左、右顶点分别为
且焦距为2,上顶点为
,且直线
的斜率之积为
.
(1)求椭圆
的方程:
(2)设直线
不经过
点且与
相交于
两点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a5abf3f257ae3e032aee7941117869.png)
(i)证明:直线
过定点
;
(ii)设
为①中点
关于
轴的对称点,过点
作直线
交于椭圆
于
两点,且
,求四边形
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03df57efff473b3cfeb8503796b7d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a5abf3f257ae3e032aee7941117869.png)
(i)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c29a7e8eea08197bf53164a560bee58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e391bf9721d27614a97bf957a94f43e.png)
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