名校
1 . 已知椭圆
的上下两个焦点分别为
,过点
与
轴垂直的直线交椭圆
于
两点,
的面积为
,椭圆
的长轴长是短轴长的
倍.
(1)求椭圆
的标准方程;
(2)已知
为坐标原点,直线
与
轴交于点
,与椭圆
交于
两个不同的点,若存在实数
,使得
,求
的取值范围,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef404abca1f78da130a38849f58559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5585a42c8f07ad90b94ace9db3d78994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74681aa6901213e672154f38ead0fa6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2019-12-03更新
|
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3卷引用:湖南省长沙市宁乡市2022-2023学年高二上学期期末数学试题
名校
2 . 已知直线l与抛物线
交于点A,B两点,与x轴交于点M,直线OA,OB的斜率之积为
.
(1)证明:直线AB过定点;
(2)以AB为直径的圆P交x轴于E,F两点,O为坐标原点,求|OE|
|OF|的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)证明:直线AB过定点;
(2)以AB为直径的圆P交x轴于E,F两点,O为坐标原点,求|OE|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
您最近一年使用:0次
2018-11-25更新
|
585次组卷
|
3卷引用:湖南省长沙市宁乡市2018-2019学年高二上学期期末理科数学试题
名校
3 . 设
分别为椭圆
的左、右焦点,点
在椭圆
上,且点
和
关于点
对称.
(Ⅰ)求椭圆
的方程;
(Ⅱ)过右焦点
的直线
与椭圆相交于
两点,过点
且平行于
的直线与椭圆交于另一点
,问是否存在直线
,使得四边形
的对角线互相平分?若存在,求出
的方程;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bba0bd73a215dfef56845811bc856d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7157a1a8271d0ae8017dec20145ad046.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)过右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e98eb6db9c24321307c445af89a855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2019-07-05更新
|
1971次组卷
|
9卷引用:湖南省长沙市雅礼中学2023-2024学年高三上学期月考(五)(1月期末)数学试卷
4 . 已知圆
:
和点
,
是圆
上任意一点,线段
的垂直平分线和
相交于点
,
的轨迹为曲线
.
(1)求曲线
的方程;
(2)点
是曲线
与
轴正半轴的交点,直线
交
于
、
两点,直线
,
的斜率分别是
,
,若
,求:①
的值;②
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7e9af961aab15303037f8b333bd6bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a44ddf4bd24eb6172aef893c734e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea629922b86da23efeb8aa83d2b91ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/2a5b321a5a214831f7a203615a4dd0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
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2018-01-03更新
|
1655次组卷
|
4卷引用:湖南省长沙市岳麓区湖南师范大学附属中学2018-2019学年高二下学期期末数学试题
解题方法
5 . 设A是圆
上的任意一点,
是过点A与
轴垂直的直线,D是直线
与
轴的交点,点M在直线
上,且满足
.当点A在圆上运动时,记点M的轨迹为曲线
.
(1)求曲线
的标准方程;
(2)设曲线
的左右焦点分别为
、
,经过
的直线
与曲线
交于P、Q两点,若
,求直线
的方程.
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/df91cfb00655492db243948145693c99.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/4c5625acf5824aab8527f2acc0bf255d.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/ef55461254f94fdb9c9b9592eac70b92.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/6d7d71de58004fda981d32a5280504b5.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/ef55461254f94fdb9c9b9592eac70b92.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/6d7d71de58004fda981d32a5280504b5.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/e2ab05b91f2b4bac94e7a0a13fba1947.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/242c7bc53cd4491e8b6c4d467bbbbbbc.png)
(1)求曲线
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/242c7bc53cd4491e8b6c4d467bbbbbbc.png)
(2)设曲线
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/242c7bc53cd4491e8b6c4d467bbbbbbc.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/816177211014411bb838ec89f0521632.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/92780370ef3446c2a451bab8907eedd3.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/92780370ef3446c2a451bab8907eedd3.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/e0b475ce6cf547e4b46367c45d5694bc.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/242c7bc53cd4491e8b6c4d467bbbbbbc.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/820e246825a64befa874989b02a5b7c2.png)
![](https://img.xkw.com/dksih/QBM/2015/5/4/1572092153012224/1572092159115264/STEM/e0b475ce6cf547e4b46367c45d5694bc.png)
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|
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