名校
解题方法
1 . 已知结论:椭圆
上一点
处切线方程为
.试用此结论解答下列问题.如图,已知椭圆
:
的右焦点为
,原点为
,椭圆的动弦AB过焦点
且不垂直于坐标轴,弦
的中点为
,椭圆
在点A,B处的两切线的交点为
.
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a271c22e34d4df61636ab3052a8e0ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1185a977aa9dc61d23db4b658126f8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa77802f9a072a800ee5098f668d5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/b9703fbb-7e2a-404b-bdfe-c1c16369ef43.png?resizew=161)
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfba099195b252ab0faba0d8360fae98.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
,
.
(1)若函数
在定义域上单调递增,求
的取值范围;
(2)若函数
有两个极值点
.
(i)求
的取值范围;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa6a40d8772bdc1becba2857272aa7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70a31c1e21548002b21b55015d361cf.png)
您最近一年使用:0次
2024-03-07更新
|
824次组卷
|
4卷引用:江苏省南京市五校2023-2024学年高二下学期期初调研测试数学试题
名校
解题方法
3 . 已知函数
.
(1)求
在
上的最大值;
(2)若关于
的不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea795d003952be199f3e6697daeb235.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20082e474b757273b4b83b13f16ddb61.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a63af57ca61555cb9d63ba6c051c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
离心率为
,椭圆上的点到焦点的最远距离是
.
(1)求椭圆
的方程;
(2)椭圆上有四个动点
,
,
,
,且
与
相交于点
.
①若点
的坐标为
,
为椭圆的上顶点,
为椭圆的右顶点,求
的斜率;
②若直线
与
的斜率均为
时,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab46ea0cba2d06283fae3d864a2329e0.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)椭圆上有四个动点
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081cd41dab0f2a8f84b0e9f1df4843fb.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/9d78abbad68bbbf12af10cd40ef4c353.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
您最近一年使用:0次
2024-03-03更新
|
1408次组卷
|
4卷引用:江苏省张家港市2023-2024学年高三下学期2月阶段性调研测试数学试卷
江苏省张家港市2023-2024学年高三下学期2月阶段性调研测试数学试卷(已下线)第3套-期初重组模拟卷(已下线)第五套 最新模拟重组精华卷(2月开学考试)湖北省黄冈市浠水县第一中学2024届高三下学期第二次模拟考试数学试题
5 . 对于数列
,若存在正数k,使得对任意
,
,都满足
,则称数列
符合“
条件”.
(1)试判断公差为2的等差数列
是否符合“
条件”?
(2)若首项为1,公比为q的正项等比数列
符合“
条件”.
①求q的取值范围;
②记数列
的前n项和为
,证明:存在正数
,使得数列
符合“
条件”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38b6286e5f74b604b9fb639c55d611f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67750b7649c47aa6dbf24e72ee7ac27d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d79a8b8500b2313a5b08a023d90b15.png)
(1)试判断公差为2的等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bf72626042d976d413196215876684.png)
(2)若首项为1,公比为q的正项等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21053f02e4b27d6cbcc91a8f6d0d33c8.png)
①求q的取值范围;
②记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed1e9cdd5a82f29ec89b2c53b4fa6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cba3bb73f0c643c79b53db038c3706a.png)
您最近一年使用:0次
6 . 已知椭圆
的右焦点为
,直线
与
相交于
、
两点.
(1)求直线l被圆
所截的弦长;
(2)当
时,
.
(i)求
的方程;
(ii)证明:对任意的
,
的周长为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7b07ace87ed58fdc1f1bc78a04aeda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6199fedebb50f6e78edf3c857a661fe.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)
(1)求直线l被圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b96eda0601673fafb836643969914f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ad7d1e3fad77908415415d6b2a90f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519471c8b171671833ad6e033ac26cea.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(ii)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3744ee15af01a8e7c0f126edb5f68132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
您最近一年使用:0次
2024-02-28更新
|
908次组卷
|
4卷引用:江苏省南通市海安高级中学2024届高三下学期开学考试数学试题
23-24高二下·江苏·开学考试
解题方法
7 . 已知函数
.
(1)若直线
与函数
的图象相切,求实数a的值;
(2)若函数
有两个极值点
和
,且
,证明:
.(e为自然对数的底数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bbe412de9506fecbaf1d9ed8b83fc17.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2fdc6fa4e8a0b98223576452e81ee28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5be3af0c67a20bee47063487d305f2.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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7766006389ba796ddfebdfcc8913a5dc.png)
您最近一年使用:0次
名校
8 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若
是
的极小值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0b99093b2f29192833128105c1b35b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-02-17更新
|
1329次组卷
|
6卷引用:江苏省扬州市扬州中学2024届高三下学期开学检测数学试题
9 . 已知点
在抛物线
的准线上,过点
作直线
与抛物线
交于
两点,斜率为2的直线与抛物线交于
两点.
(1)求抛物线
的标准方程;
(2)① 求证:直线
过定点
;
② 若
的面积为
,且满足
,求直线
斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc2de9df8bce6139613bb86322db0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e478787ebfeb68a5a7594dbd9eecd4.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)① 求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
② 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c8bef41fa6778e5eb57e2f19ea48f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-01-27更新
|
262次组卷
|
3卷引用:江苏省徐州市沛县第二中学2024届高三下学期期初测试数学试题
江苏省徐州市沛县第二中学2024届高三下学期期初测试数学试题湖北省武汉外国语学校2023-2024学年高二上学期期末考试数学试题(已下线)2.4.2 抛物线的性质(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
解题方法
10 . 已知椭圆
的离心率为
,抛物线
在第一象限与椭圆
交于点
,点
为抛物线
的焦点,且满足
.
(1)求椭圆
的方程;
(2)设直线
与椭圆
交于
,
两点,过
,
分别作直线
的垂线,垂足为
、
,
与
轴的交点为
.若
、
、
的面积成等差数列,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e48d1edbfb6a5a48f9a95551d1dbc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c7fc8e284e4aafd93a630d50a53930.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212c59b6ab1e256b363fc1f1ff3f5fbe.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303094682b317daea83be885d1c7ff4b.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/acc290b44635265137fdf13146b6a6d9.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/9fac56192b8a935a1a0d9ba9ddea0253.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2024-01-25更新
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4卷引用:江苏省扬州市扬州中学2024届高三下学期开学检测数学试题