名校
解题方法
1 . 设椭圆
的左右焦点分别为
,
,焦距为
,点
在椭圆的内部,点P是椭圆上的动点,且
恒成立,则椭圆的离心率的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82fe25db889399bb3ca4ffd5dd5db84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/501daf0a108d8d7a7a36cf54dedf200a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a75d36d6aea9e5d37ff8001a368e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e82018b4636ee48dfc7921a590017a5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2 . 已知椭圆E:
(
)的离心率是
,
,
分别为椭圆E的左右顶点,B为上顶点,
的面积为2.直线l过点
且与椭圆E交于P,Q两点(P,Q异于
,
)
(1)求椭圆E的标准方程;
(2)求
的面积最大值;
(3)设直线
与直线
的斜率分别为
,
,求证:
为常数,并求出这个常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737029b90a384c2b48973b84bfe74b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d776a89f4fd29dccffe1040069d59ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
(1)求椭圆E的标准方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45b8b000c9c286bff8a480dbf03b513.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.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/67351fe10fcfc3f9072eec4c60bfaaa5.png)
您最近一年使用:0次
2020-03-25更新
|
311次组卷
|
2卷引用:江苏省南通市海门中学2019-2020学年高二上学期期中数学试题
解题方法
3 . 如图,在平面直角坐标系
中,已知椭圆
的离心率为
且右焦点
到右准线
的距离为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/70259ee7-4ec3-4123-a11c-872e850294ec.png?resizew=159)
(1)求椭圆
的标准方程:
(2)过点
的直线与椭圆
交于
两点,与
交于点
是弦
的中点,直线
与
交于点
.若
与
的面积之比是
,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/70259ee7-4ec3-4123-a11c-872e850294ec.png?resizew=159)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0664a68104a5370205d9d0a80d8862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6025da1f98c4e9aa6454dc535dd426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985b383be47791e0409e542225982299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
4 . 如图所示,在平面直角坐标系
中,点
是抛物线
上的点,直线
交直线
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b939912a-70c3-4105-b6b7-8f31407db036.png?resizew=155)
(1)求
长度的最小值;
(2)若点
也是抛物线
上的点,且
,直线
交直线
于点
.求四边形
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd24f3c4bc9f9a75d4b28630bb630d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b939912a-70c3-4105-b6b7-8f31407db036.png?resizew=155)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dcca60ba6144abbf47abd51d1f63f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd24f3c4bc9f9a75d4b28630bb630d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
解题方法
5 . 抛物线
和圆
,直线
与抛物线
和圆
分别交于四个点
、
、
、
(自上而下的顺序为
、
、
、
),则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdf4c156db6058d8e8b913f5c77fcdf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6c6b732ae192f2ce8fc341b5bc9627.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026808536f6b6d265c778e23836fbf13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/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/be1382d5ef5b6750508397bfca2cb53e.png)
您最近一年使用:0次
2020-02-15更新
|
858次组卷
|
6卷引用:2020届江苏省如皋、如东高三上学期期中数学试题
2020届江苏省如皋、如东高三上学期期中数学试题2019年重庆市三模数学理科试题2019届重庆市九龙坡区育才中学高三学业质量调研抽测(第三次5月)理科数学试题人教B版(2019) 选择性必修第一册 过关斩将 第二章 平面解析几何 2.8 综合拔高练(已下线)3.3.2 抛物线的简单几何性质(2)(基础练)-2020-2021学年高二数学十分钟同步课堂专练(人教A版选择性必修第一册)(已下线)专题8 求定点定值运算(提升版)
6 . 已知一族双曲线
:
(
,且
),设直线
与
在第一象限内的交点为
,由
向
的两条渐近线作垂线,垂足分别为
,
.记
的面积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4bc0200e3fa77dce28106d44bcfb8e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb1a45109c82237e6051d039e5bde04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7692514a24939fee3c3fed6e699cbd64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed9b981aebc8c09de65e4bf84b8f0f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4bc0200e3fa77dce28106d44bcfb8e.png)
您最近一年使用:0次
7 . 如图,已知椭圆
,左、右焦点分别为
,
,右顶点为
,上顶点为
,
为椭圆上在第一象限内一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/aac8755e-159d-42c3-bd4d-d76b062d7f2a.png?resizew=230)
(1)若
.
①求椭圆的离心率
;
②求直线
的斜率.
(2)若
,
,
成等差数列,且
,求直线
的斜率的取值范围.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/aac8755e-159d-42c3-bd4d-d76b062d7f2a.png?resizew=230)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d87fd50f35d766279f41384c7bb81d.png)
①求椭圆的离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
②求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b3a51deb7af25837ccefcf10eb1262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a87481122e5e2714e1e25f85e248a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbac9a87d39df24f7b357890b532718b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bf40fe48f416db0e0f215ce7cd5286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
您最近一年使用:0次
8 . 点
为椭圆
上一点,
、
分别是圆
和
上的动点,则
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.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/4e892ccfb382cdd5ee5dbb710542b1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837fbc4862ae7c699199535d991234a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bb1548ddc0e5536a35b1bd78c4e7cd.png)
您最近一年使用:0次
2020-01-31更新
|
846次组卷
|
5卷引用:江苏省常州市2019-2020学年高二上学期期末数学试题
江苏省常州市2019-2020学年高二上学期期末数学试题(已下线)专题10 椭圆方程及其简单几何性质中档题突破-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)(已下线)专题3.2 椭圆及其标准方程-重难点题型检测-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)3.1 椭圆(已下线)3.1.1 椭圆及其标准方程【第一课】“上好三节课,做好三套题“高中数学素养晋级之路
9 . 如图,在三棱锥
中,
,
平面
,
,
,点
、
分别为
,
的中点,点
在线段
上.若
,则异面直线
与
所成角的余弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/7a69e7ee-d692-4175-a4ba-2db27e5d12cd.png?resizew=117)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9832f67cb002bf430dca54c2786ae4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6d39135a2f8472d66ea00eda3b13ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434845564fd5765244f8d1aa9240fa39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441c1291b182a80d0e78079b669e696c.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386e945cb8ffa5288ba68b0714ea9e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/7a69e7ee-d692-4175-a4ba-2db27e5d12cd.png?resizew=117)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
10 . 已知
为椭圆
:
的右焦点,点
,
,
为椭圆
上三点,当
时,称
为“和谐三角形”,则“和谐三角形”有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
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A.0个 | B.1个 | C.3个 | D.无数个 |
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2020-01-31更新
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502次组卷
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2卷引用:江苏省常州市2019-2020学年高二上学期期末数学试题