名校
1 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
的短轴长等于
,离心率为
,
、
分别为椭圆
的上、下顶点.
(Ⅰ)求椭圆
的方程;
(Ⅱ)设
为直线
不同于点
的任意一点,若直线
、
分别与椭圆相交于异于
、
的点
、
,证明:
恒为钝角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb223b8777ab973970491bf0dcc6806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de72a5190834f5dbe895596656c038b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1156a8b29780810bd472f6d9e11b0e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358c69b4f6c350c35d19d33c69f2a2a8.png)
您最近一年使用:0次
解题方法
2 . 已知
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62430466e50da4a5bd32783040b04bfc.png)
(1)求
;
(2)当k为何实数时,
与
的夹角为钝角?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72570757db98eae7543a123d47d829e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62430466e50da4a5bd32783040b04bfc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a426c9d5ee25068b1a7cc223b47382.png)
(2)当k为何实数时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea1f268299d57e5362182760a5961af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3364b5989fa241b26266c0d96ab9714.png)
您最近一年使用:0次
16-17高二上·上海浦东新·阶段练习
名校
3 . 已知
,
,
与
的夹角为45°,若向量
与
的夹角为锐角时,则
的取值范围为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc9e508a2f476c8ade3562f0801ff57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ace13ebf9148c275e0b1f0ac5f5b6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7447872b1ead17d89c0947b601cd87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f075f5f31c260c7ac96d58c23bd8997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2020-01-30更新
|
347次组卷
|
5卷引用:上海市华东师范大学第二附属中学2016-2017学年高二上学期第一次月考数学试题2
(已下线)上海市华东师范大学第二附属中学2016-2017学年高二上学期第一次月考数学试题2湖北省黄冈市蕲春县第一高级中学2020-2021学年高一下学期3月月考数学试题云南省大理州宾川县第四完全中学2020-2021学年高一4月月考数学试题湖北省黄冈市麻城市第二中学2020-2021学年高一下学期4月月考数学试题湖南省株洲市南方中学2020-2021学年高一下学期4月月考数学试题
4 . 如图,在平面直角坐标系中,点
,
,锐角
的终边与单位圆O交于点P.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/30f8986f-47ff-4d8e-86e7-cccdb6284f41.png?resizew=166)
(Ⅰ)当
时,求
的值;
(Ⅱ)在
轴上是否存在定点M,使得
恒成立?若存在,求出点M坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9ac996c3ee6b505a1061ad13a96177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d26d0ade4635afddc9c7af4ece68920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/30f8986f-47ff-4d8e-86e7-cccdb6284f41.png?resizew=166)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97debbb1d8999897152876666108590d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(Ⅱ)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5f4ed6e9349ed987908a84e0ced7a6.png)
您最近一年使用:0次
2019-02-06更新
|
712次组卷
|
3卷引用:【市级联考】湖北省荆门市2018-2019学年高一上学期期末学业水平阶段性检测数学试题
5 . 圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
:与
轴正半轴交点为
,圆
上的点
,
分别位于第一、二象限,并且
,若点
的坐标为
,则点
的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.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/1dde8112e8eb968fd042418dd632759e.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/2975b674bfdf04a79aef76074502a7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1e83636eced5626383c99faeb44e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
6 . 设
的外心
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a27dc396251a4453094d19baa79816.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e745e7394aa9d9cfa980f8766ad1661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a27dc396251a4453094d19baa79816.png)
您最近一年使用:0次
2019-01-11更新
|
903次组卷
|
3卷引用:【市级联考】湖南省株洲市2019届高三教学质量统一检测(一)理科数学试题
7 . 已知椭圆
的左、右顶点分别是点A,B,右焦点是F,过F点作直线与长轴垂直,与椭圆交于P,Q两点.
(1)若∠PBF=60°,求椭圆的离心率;
(2)求证:∠APB一定为钝角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665489f3abfc49ce2f41989bc4ce2ba2.png)
(1)若∠PBF=60°,求椭圆的离心率;
(2)求证:∠APB一定为钝角.
您最近一年使用:0次
14-15高三上·内蒙古·期中
名校
8 . 已知不共线向量
夹角为
,
,
,
,
,
在
处取最小值,当
时,
的取值范围为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870621330877caa08df79df91fc4ff4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1181366d40666079a73496076c382f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07293a24cf2d403f59aa43aaacb8e236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5dd33175846c7e799e99fd0ad30ecf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797174f24f10bebffc0e125547153cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df12c60531c3f1ad7b4f182f3fe4b96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82120861c1c4f7cc1a7a3f169f082a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f19f7927e2734c146aeffd81e53e5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-10-16更新
|
1576次组卷
|
11卷引用:2015届内蒙古一机一中高三上学期期中考试理科数学试卷
(已下线)2015届内蒙古一机一中高三上学期期中考试理科数学试卷【市级联考】山东省潍坊市2019届高三下学期高考模拟(一模)考试数学(理科)试题【市级联考】山东省潍坊市2019届高三下学期高考模拟(一模)考试数学(文科)试题(已下线)专题5.4 平面向量的综合应用(练)【理】—《2020年高考一轮复习讲练测》2020届山东省枣庄市第八中学东校区高三一调模拟考试数学试题(已下线)备战2020年高考数学之考场再现(山东专版)04(已下线)专题16 平面向量的数量积-冲刺2020高考跳出题海之高三数学模拟试题精中选萃辽宁省辽宁师范大学附属中学2019-2020学年高一下学期期末数学试题江苏省无锡市天一中学2020-2021学年高一(强化班)上学期期末数学试题江苏省新区实验2020-2021学年高一下学期期中数学试题江苏省苏州市实验中学2020-2021学年高一下学期期中数学试题
9 . 已知直线y=2x上一点P的横坐标为a,有两个点A(-1,1),B(3,3),那么使向量
与
夹角为钝角的一个充分不必要条件是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d956b09c004ddf8bdf6669a8182e80ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e287cd7e75c3199af6f935492c947a.png)
A.-1<a<2 | B.0<a<1 | C.-![]() ![]() | D.0<a<2 |
您最近一年使用:0次
2018-06-26更新
|
316次组卷
|
2卷引用:湖北省荆州成丰学校2017-2018学年高二3月月考文科数学试题
10 . 设两个向量
,满足
,
的夹角为60°,若向量
与向量
的夹角为钝角,则实数
的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad59ee7969f2a082ed53bdf0aaa748ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e767cd59ad5388bf5453205a8519a631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad59ee7969f2a082ed53bdf0aaa748ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963022da5770fc8d051cdc6fdac6ef06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a62d2b1971615e6e8d18bf3f89eedee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2018-08-13更新
|
981次组卷
|
5卷引用:【全国百强校】北京东城区北京二中2016-2017学年高一下学期期中考试数学试题