1 . 已知椭圆
的左、右顶点分别为
,右焦点为
,过点
且斜率为
的直线
交椭圆
于点
.
(1)若
,求
的值;
(2)若圆
是以
为圆心,1为半径的圆,连接
,线段
交圆
于点
,射线
上存在一点
,使得
为定值,证明:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcb166b53a49e393871bcb14a528792.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/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d846d0c16bda5882bbb8a557de733c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01adc01f96d2957a3806b2a3893ff7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2 . 已知椭圆E:
的离心率为
,其左、右焦点分别为
,
,T为椭圆E上任意一点,
面积的最大值为1.
(1)求椭圆E的标准方程;
(2)过点
的直线与椭圆E交于B,C两点,过点B,C分别作直线l:
的垂线(点B,C在直线l的两侧).垂足分别为M,N,记
,
,
的面积分别为
,
,
,试问:是否存在常数t,使得
,
,
总成等比数列?若存在,求出t的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfbfcfe248439929f0b33f712471b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.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/c820e30560907adc6ad54b2918011e8e.png)
(1)求椭圆E的标准方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6074f4beb31fb393ae3978e0035ae16f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23b488f961d9fde37feb7f5c497c0d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351dedd9707c0406837e79a1f638a5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1262db728289746a31dc4481eac1728f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
您最近一年使用:0次
名校
3 . 若点A,F分别是椭圆
的左顶点和左焦点,过点F的直线交椭圆于M,N两点,记直线
的斜率为
,其满足
,则直线
的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79275f21738e7f001df5ebe6632bfe3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe0ea445fc6b756b34b56a95e4d0381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a745c2da749f30fcf58edf0821f7cb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa29fe6cd9eb51c184f6299d437375cb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2018-11-28更新
|
3068次组卷
|
4卷引用:【全国百强校】湖北省武汉市华中师范大学第一附属中学2018-2019学年高二上学期期中检测数学(理)试题