名校
1 . 如图,已知
,
分别是椭圆![](https://img.xkw.com/dksih/QBM/2015/4/7/1572064412966912/1572064419102720/STEM/5a58530aaadd4a689f14b831ed96ffb8.png)
的左、右焦点,过
与
轴垂直的直线交椭圆于点
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26506b1009f26398205059007e95dcb6.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572064412966912/1572064419102720/STEM/bf901824ba504b3eaa8283dee2df0979.png)
(1)求椭圆的标准方程;
(2)已知点
,问是否存在直线
与椭圆交于不同的两点
,
,且
的垂直平分线恰好过
点?若存在,求出直线
斜率的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572064412966912/1572064419102720/STEM/5a58530aaadd4a689f14b831ed96ffb8.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572064412966912/1572064419102720/STEM/fc311fce86c24c3ca1e001bc9be3b4ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8c8f7bd39a507dbf1634a3857b3c30.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/26506b1009f26398205059007e95dcb6.png)
![](https://img.xkw.com/dksih/QBM/2015/4/7/1572064412966912/1572064419102720/STEM/bf901824ba504b3eaa8283dee2df0979.png)
(1)求椭圆的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333160ac2088b2f83ac1e0c446b5d8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2016-12-03更新
|
956次组卷
|
2卷引用:2014-2015学年山东省济南第一中学高二上学期期末考试数学试卷
11-12高三上·云南红河·阶段练习
2 . 如图,曲线
是以原点O为中心、
为焦点的椭圆的一部分,曲线
是以O为顶点、
为焦点的抛物线的一部分,A是曲线
和
的交点
且
为钝角.
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037241856/STEM/2bdd357090ad4775843cd6bfbd681cf1.png)
(1)求曲线
和
的方程;
(2)过
作一条与
轴不垂直的直线,分别与曲线
依次交于B、C、D、E四点,若G为CD中点、H为BE中点,问
是否为定值?若是求出定值;若不是说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ceb0061dbf8f720f8d0bee5ca5c822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0613f3bc4f0cd9f81cbb7ebf5f4ae9.png)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037241856/STEM/2bdd357090ad4775843cd6bfbd681cf1.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037241856/STEM/364510c64a3d410c8244439a74ca99d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86404c0a62742241d6d772b9cb657b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c37a89b5adc2eb1aba1f37fab2bd12.png)
您最近一年使用:0次
11-12高三·山东烟台·期末
3 . 已知在平面直角坐标系
中,向量
的面积为
,且
,
.
(1)设
,求向量
与
的夹角
的取值范围;
(2)设以原点
为中心,对称轴在坐标轴上,以
为右焦点的椭圆经过点
,且
,当
取最小值时,求椭圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2031522e069b401e327110e535993fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb99c1873bfb3d6ed1aeab59179c2780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26337f5eab93cf705e9805dc9fc53c64.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9dd2c797c73a36923ed5abfd673da6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08493c1e001d85731cb4863ec38857fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f064ba4502a9845a3f06835514f5a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)设以原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/8961b74ace912806f3c6af8ceaf5cfec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f0e6d3115e900f1a359ec4f894e8896.png)
您最近一年使用:0次