名校
解题方法
1 . 如图,在平面直角坐标系
中,离心率为
的椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
的左顶点为
,过原点
的直线(与坐标轴不重合)与椭圆
交于
两点,直线
分别与
轴交于
两点.若直线
斜率为
时,
.
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572055058956288/1572055065116672/STEM/d7f7d7c87d8e4053a956d1b46bf049d6.png)
(1)求椭圆
的标准方程;
(2)试问以
为直径的圆是否经过定点(与直线
的斜率无关)?请证明你的结论.
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572055058956288/1572055065116672/STEM/e36d417511b248bba30c49ee6faa620c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ec56b59d6f2654570c2b5c4fd13a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9bd788d2944327dd8d25047a08eea54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355c8e295cd0e7895a7bcabb31ebcf13.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572055058956288/1572055065116672/STEM/d7f7d7c87d8e4053a956d1b46bf049d6.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)试问以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2016-12-03更新
|
1213次组卷
|
7卷引用:2015届江苏省泰州市高三上学期期末考试理科数学试卷
2010·北京·二模
解题方法
2 . 已知椭圆
和圆
:
,过椭圆上一点P引圆O的两条切线,切点分别为A,B.
![](https://img.xkw.com/dksih/QBM/2013/6/28/1571259842387968/1571259847589888/STEM/a69117e79c5548af95ff12f69faa99e1.png?resizew=328)
(1)(ⅰ)若圆O过椭圆的两个焦点,求椭圆的离心率e的值;
(ⅱ)若椭圆上存在点P,使得
,求椭圆离心率e的取值范围;
(2)设直线AB与x轴、y轴分别交于点M,N,问当点P在椭圆上运动时,
是否为定值?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4ab88bc995ac5fc57518930a03c534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://img.xkw.com/dksih/QBM/2013/6/28/1571259842387968/1571259847589888/STEM/a69117e79c5548af95ff12f69faa99e1.png?resizew=328)
(1)(ⅰ)若圆O过椭圆的两个焦点,求椭圆的离心率e的值;
(ⅱ)若椭圆上存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df9b574c6b6a4c878bf425d4fa31d66.png)
(2)设直线AB与x轴、y轴分别交于点M,N,问当点P在椭圆上运动时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad3e95a9b0223e280a9034a91b29fbc.png)
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11-12高三上·江苏泰州·期末
3 . 已知椭圆的中心在坐标原点,焦点在
轴上,以其两个焦点和短轴的两个端点为顶点的四边形是一个面积为4的正方形,设
为该椭圆上的动点,C、D的坐标分别是
,则
的最大值为_______
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668093952/STEM/b6c5a899315a43529f7d81897aa69b95.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668093952/STEM/6c2e05414dfc4cddae4a3090a2f74748.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e771e89512a51a6e1ebf954b19aab9d.png)
![](https://img.xkw.com/dksih/QBM/2011/11/21/1570357662908416/1570357668093952/STEM/1395821ed9af42de895580fa14941187.png?resizew=83)
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11-12高三上·江苏泰州·期末
解题方法
4 . 在三棱锥
中,平面
平面
,
为正三角形,
,
,
(1)求
与
所成角的余弦值;
(2)在平面
中求一点
,使得
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0ad6e27ea2d5d028f0f76043ccb1f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c65edad25ddd666cdce0d7e5afefc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7422660f0635be92e11838af5f4b4b5e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e245440d3761fb4217eaa8dc303fa288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
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