名校
1 . 在平面直角坐标系xOy中,椭圆C:
(a>b>0)的上顶点到焦点的距离为2,离心率为
.
(1)求a,b的值.
(2)设P是椭圆C长轴上的一个动点,过点P作斜率为k的直线l交椭圆C于A、B两点.
(ⅰ)若k=1,求△OAB面积的最大值;
(ⅱ)若PA2+PB2的值与点P的位置无关,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求a,b的值.
(2)设P是椭圆C长轴上的一个动点,过点P作斜率为k的直线l交椭圆C于A、B两点.
(ⅰ)若k=1,求△OAB面积的最大值;
(ⅱ)若PA2+PB2的值与点P的位置无关,求k的值.
您最近一年使用:0次
2016-12-03更新
|
913次组卷
|
7卷引用:2015届江苏省宿迁市重点中学高三下学期期初开学联考理科数学试卷
2014高三·全国·专题练习
2 . 设a,b∈R,若x≥0时恒有0≤x4﹣x3+ax+b≤(x2﹣1)2,则ab等于___________ .
您最近一年使用:0次
2016-12-03更新
|
2703次组卷
|
7卷引用:2020届江苏省南京市第二十九中高三下学期3月期初数学试题
2020届江苏省南京市第二十九中高三下学期3月期初数学试题(已下线)2014届人教版高考数学文科二轮专题复习提分训练10练习卷2013年普通高等学校招生全国统一考试文科数学(浙江卷)河北省定州中学2017届高三(高补班)下学期第二次月考(4月)数学试题浙江省绍兴市诸暨中学2020-2021学年高二(平行班)下学期4月期中数学试题(已下线)考点05 导数与不等式-2022年高考数学(文)一轮复习小题多维练(全国通用)(已下线)模块二 大招14 共零点问题
13-14高三下·江苏盐城·开学考试
解题方法
3 . 如图,
是椭圆
的左、右顶点,椭圆
的离心率为
,右准线
的方程为
.
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/2e1f417e79204574a4ee13109aad3686.png)
(1)求椭圆方程;
(2)设
是椭圆
上异于
的一点,直线
交
于点
,以
为直径的圆记为
. ①若
恰好是椭圆
的上顶点,求
截直线
所得的弦长;
②设
与直线
交于点
,试证明:直线
与
轴的交点
为定点,并求该定点的坐标.
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/4b058e9429e544bb9cbd39cd9dacbc53.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/b0826282603f4972b0816752780cebf4.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/d956d8f3c2a443c4b05b98a922da42ed.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/07b8ba1f5a6c48709776f86c9b1018de.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/f8fc5c263ae842aeadea20a4d2ca7996.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/e3b9ed8c129b4d4bb10a295b7f03c9ad.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/2e1f417e79204574a4ee13109aad3686.png)
(1)求椭圆方程;
(2)设
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/246f21f786064ad9bcc9001266c057b1.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/d956d8f3c2a443c4b05b98a922da42ed.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/4b058e9429e544bb9cbd39cd9dacbc53.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/29b15b9b0e454e2b8fe22b9b52ada11a.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/f8fc5c263ae842aeadea20a4d2ca7996.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/4dacb2fc3f8a4322ab5a8e420b4c5787.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/04363209f24c4a98ac3879c1a42861a5.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/ec27ac349c9a4a46b331f09694200ff5.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/246f21f786064ad9bcc9001266c057b1.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/d956d8f3c2a443c4b05b98a922da42ed.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/d7d8276e126f49d9a95376a52a8f9ecc.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/cd8dd597d05a46dfb01e1dfe4ce85ca8.png)
②设
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/ec27ac349c9a4a46b331f09694200ff5.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/273b4edb0a294f4da7371494b3946a32.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/92330d0b64ca439c865e866c3c3c58e1.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/770d2a2dd4c64933ac34691f7465f4ac.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/49c6503825464161b0ce4dacf700e11c.png)
![](https://img.xkw.com/dksih/QBM/2014/3/5/1571545934913536/1571545940459520/STEM/db0bbef4f6874034baacf2578dc860cd.png)
您最近一年使用:0次
12-13高三·江苏扬州·开学考试
名校
4 . 已知
是实数,函数
,
和
,分别是
的导函数,若
在区间
上恒成立,则称
和
在区间
上单调性一致.
(Ⅰ)设
,若函数
和
在区间
上单调性一致,求实数
的取值范围;
(Ⅱ)设
且
,若函数
和
在以
为端点的开区间上单调性一致,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://img.xkw.com/dksih/QBM/2013/9/10/1571350171623424/1571350177316864/STEM/730c4b9250474099bd10150d50d0fe1c.png?resizew=192)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51350a90203fcdc2d500a89061b7f52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0ed188d083966baaae94e6b86064f9.png)
![](https://img.xkw.com/dksih/QBM/2013/9/10/1571350171623424/1571350177316864/STEM/8a6828b27fe14b68832e6f72a97ddde2.png?resizew=96)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
(Ⅰ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://img.xkw.com/dksih/QBM/2013/9/10/1571350171623424/1571350177316864/STEM/2b1a6693b07b4fd881c668d2c5d5e81a.png?resizew=57)
![](https://img.xkw.com/dksih/QBM/2013/9/10/1571350171623424/1571350177316864/STEM/2c77e82d58b5460fb3b9aff60236a5cc.png?resizew=13)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://img.xkw.com/dksih/QBM/2013/9/10/1571350171623424/1571350177316864/STEM/c976db6864934c19965eef3c6d76da6d.png?resizew=40)
您最近一年使用:0次
11-12高三下·山东潍坊·假期作业
解题方法
5 . 已知椭圆
的左、右焦点分别为
、
, 点
是椭圆的一个顶点,
是等腰直角三角形.
(Ⅰ)求椭圆的方程;
(Ⅱ)过点
分别作直线
,
交椭圆于
,
两点,设两直线的斜率分别为
,
,且
,证明:直线
过定点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/15ed90ebf0061c8a79beed307fc1719a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f9a699aededce0ad803bf8257fbbcb.png)
(Ⅰ)求椭圆的方程;
(Ⅱ)过点
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/c2b1bd378406bcd8156a56469f9300f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ebf12be9314c6bfb2bbf13b7bfcceb.png)
您最近一年使用:0次
11-12高三下·江苏·开学考试
解题方法
6 . 已知椭圆
中心为
,右顶点为
,过定点
作直线
交椭圆于
两点.
(1)若直线
与
轴垂直,求三角形
面积的最大值;
(2)若
,直线
的斜率为
,求证:
;
(3)在
轴上,是否存在一点
,使直线
和
的斜率的乘积为非零常数?若存在,求出点
的坐标和这个常数;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7c42003ebd00fa633c386b08c68d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72152329fb518ac828ea7056469f256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9392f80c843de7de343188e7428caa06.png)
(3)在
![](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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
11-12高三下·江苏淮安·开学考试
名校
7 . 已知
.
(1)若函数
在区间
上有极值,求实数
的取值范围;
(2)若关于
的方程
有实数解,求实数
的取值范围;
(3)当
,
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5220c1d29955df47343122a463c46a92.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b6bec0e5c57dc0c97d2581012d2c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cf6b77ccc80b271e6b41231c740da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e6a4a1d228a9eec9db8080bef34231.png)
您最近一年使用:0次
2016-12-01更新
|
1340次组卷
|
3卷引用:2012届江苏省淮阴中学高三下学期数学综合练习(1)
(已下线)2012届江苏省淮阴中学高三下学期数学综合练习(1)江苏省淮安市淮阴中学2019-2020学年高三下学期4月综合测试数学试题江苏省盐城市滨海中学2019-2020学年高二下学期期末模拟数学试题
10-11高三·江苏·单元测试
解题方法
8 . 已知函数
.
(1)求证:函数
在点
处的切线恒过定点,并求出定点坐标;
(2)若
在区间
上恒成立,求
的取值范围;
(3)当
时,求证:在区间
上,满足
恒成立的函数
有无穷多个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbece897696948bc5081d52361e2f50.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86209a88158e6e388b59b9a909da3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51947e18ac12b186aa3c09e62c036af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d28d4330fd2169fbfbbac5f5a95c074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
您最近一年使用:0次
11-12高三上·河南洛阳·期末
名校
9 . 设F1, F2分别为双曲线
的左、右焦点,P为双曲线右支上任一点,若
的最小值为
,则该双曲线的离心率的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373cf457a0c1676b861a431ff05bc12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1f29aa1cc69310e7e7068ee9ebbb13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17cd7223f1384160818fc1c74544c485.png)
A.(1,![]() | B.(1,3) | C.(1,3] | D.[![]() |
您最近一年使用:0次
2016-11-30更新
|
1880次组卷
|
5卷引用:江苏省扬州中学2020-2021学年高二下学期开学考试数学试题
江苏省扬州中学2020-2021学年高二下学期开学考试数学试题(已下线)2011届河南省洛阳市高三上学期期末考试理科数学辽宁省辽阳市七校联合体2019-2020学年高三上学期12月份月考理科数学试题重庆市杨家坪中学2021届高三下学期第二次月考数学试题(已下线)专题 3.3 双曲线性质归类(2)