名校
1 . 已知函数
,
,
.
(1)当
时,讨论函数
的零点个数.
(2)
的最小值为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9de719dcc4468ca5b923581a63a0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae88190d80c2bc109449fe8852a4c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08390369ffbdc53a8c75c351b5750120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9de719dcc4468ca5b923581a63a0c5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3c2be7482719651bcf491949681e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07b3598ead92435898950756adb369f.png)
您最近一年使用:0次
2019-05-17更新
|
1780次组卷
|
9卷引用:浙江省衢州二中2020届高三下学期6月模拟数学试题
2 . 已知椭圆
过点
,且它的离心率为
,直线
与椭圆
相交于
,
两点.
(Ⅰ)求椭圆
的方程;
(Ⅱ)若弦
的中点
到椭圆
中心的距离为1,求弦长
的最大值;
(Ⅲ)过原点
作直线
,垂足为
,若
,
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f04443a0c1cf4808aea741c9f9379b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)若弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](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/aaff41080fdea43eea7efedf9ebc1498.png)
(Ⅲ)过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c51f1dbfa7326961a1c2fc13fdb4a64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b9deacc51ed40b7d5cd56ad21757e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a4d987663ac1ac9ef1e0429deda7fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
3 . 已知函数
有两个零点
.
(1)求
的取值范围;
(2)是否存在实数
, 对于符合题意的任意
,当
时均有
?
若存在,求出所有
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965745e702f724d0400592350e52ede1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ecd40642e5de70dad10308697517cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73c865654a32d59ab0a191363ef9254.png)
若存在,求出所有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2018-02-09更新
|
866次组卷
|
2卷引用:2020届浙江省衢州二中高三下学期第一次模拟考试数学试题
名校
4 . 已知点
是圆
上任意一点,过点
作
轴的垂线,垂足为
,点
满足
记点
的轨迹为曲线
.
(Ⅰ)求曲线
的方程;
(Ⅱ)设
,点
在曲线
上,且直线
与直线
的斜率之积为
,求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173719412736/1572173725753344/STEM/f8c257f0b9ee4927bf416c88e0fcd5d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725141c89e588830d50fb741fff4c231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173719412736/1572173725753344/STEM/e114972f72b94ab9986b840fb88f4425.png)
(Ⅰ)求曲线
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173719412736/1572173725753344/STEM/e114972f72b94ab9986b840fb88f4425.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a2b8b43e1fe82fc439d145e91b860c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173719412736/1572173725753344/STEM/e114972f72b94ab9986b840fb88f4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f1407e16443688949ac65941e871d64.png)
您最近一年使用:0次
2016-12-03更新
|
1286次组卷
|
2卷引用:2014-2015学年浙江省江山实验中学高二1月教学质检理科数学试卷
2012·吉林长春·一模
5 . 已知椭圆
、抛物线
的焦点均在
轴上,
的中心和
的顶点均为原点
,从每条曲线上取两个点,
将其坐标记录于下表中:
(Ⅰ)求
,
的标准方程;
(Ⅱ)请问是否存在直线
满足条件:①过
的焦点
;②与
交于不同两点
,
,且满足
?
若存在,求出直线
的方程;若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/aa41542b2706458d9505eae30c206cb6.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/d73dfda1236c41759f68490c0aff8219.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/61da92e53d524fef935e125f422a62a9.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/aa41542b2706458d9505eae30c206cb6.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/d73dfda1236c41759f68490c0aff8219.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/c1b9f987345247e3a07f2c3133bc8b4a.png)
将其坐标记录于下表中:
x | 3 | ![]() | 4 | ![]() |
![]() | ![]() | 0 | ![]() | ![]() |
(Ⅰ)求
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/aa41542b2706458d9505eae30c206cb6.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/d73dfda1236c41759f68490c0aff8219.png)
(Ⅱ)请问是否存在直线
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/afbcb3ca569846069869e8a0f20bb497.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/d73dfda1236c41759f68490c0aff8219.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/6dc4896a9ab848d1852abe7de86537ef.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/aa41542b2706458d9505eae30c206cb6.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/20cd3c85125140d6997887112af1a366.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/c5401bc8bb574fd5a1ad120191abc8c2.png)
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/750cbc53f9cc4cc9b12c187d12e85409.png)
若存在,求出直线
![](https://img.xkw.com/dksih/QBM/2015/7/9/1572173908058112/1572173914177536/STEM/afbcb3ca569846069869e8a0f20bb497.png)
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