11-12高二上·广东·期中
1 . 已知椭圆
(
),圆
:
,过椭圆上任一与顶点不重合的点
引圆
的两条切线,切点分别为
,直线
与
轴、
轴分别交于点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7afd4f4b2db8b0a6f06b184cc5a5efca.png)
_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://img.xkw.com/dksih/QBM/2011/12/2/1570554536484864/1570554541785088/STEM/34ee33891a764c018f74a871cb82381f.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://img.xkw.com/dksih/QBM/2011/12/2/1570554536484864/1570554541785088/STEM/0973019d0ffe41deae3550e4bb4b97c5.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/12/2/1570554536484864/1570554541785088/STEM/34ee33891a764c018f74a871cb82381f.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2011/12/2/1570554536484864/1570554541785088/STEM/fd3fd5d86f6a4362b2d231a6af631f25.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2011/12/2/1570554536484864/1570554541785088/STEM/ced35693e6d8488cbc62df51e9416a41.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2011/12/2/1570554536484864/1570554541785088/STEM/26ab7fcf3874487baa444ebce2d9ebce.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2011/12/2/1570554536484864/1570554541785088/STEM/f83989f5850c46938789e4d7748c8f49.png?resizew=15)
![](https://img.xkw.com/dksih/QBM/2011/12/2/1570554536484864/1570554541785088/STEM/f5a96ef87ca14ffba82a268f1a47f717.png?resizew=40)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7afd4f4b2db8b0a6f06b184cc5a5efca.png)
您最近一年使用:0次
2014·吉林长春·二模
名校
解题方法
2 . 已知椭圆
的右焦点为
,点
在椭圆上.
(Ⅰ)求椭圆的方程;
(Ⅱ)点
在圆
上,且
在第一象限,过
作
的切线交椭圆于
两点,问:
的周长是否为定值?若是,求出定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8258e1bdc1793aacfc4475216db39cf6.png)
(Ⅰ)求椭圆的方程;
(Ⅱ)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d84dff60278a1a7a3ee5b12c0ad313.png)
您最近一年使用:0次
2016-12-02更新
|
3071次组卷
|
11卷引用:2016-2017学年江西省九江市重点高中高二下学期第一次段考数学(理)试卷
2016-2017学年江西省九江市重点高中高二下学期第一次段考数学(理)试卷(已下线)2014届吉林省长春市高中毕业班第二次调研测试理科数学试卷2016届吉林省实验中学高三上学期第一次模拟理科数学试卷12016届吉林省实验中学高三上学期第一次模拟理科数学试卷22015-2016学年河北石家庄一中高二下第一次月考理数学卷2016届天津市耀华中学高三一模考试数学(理)试卷2016-2017学年湖北省孝感市七校教学联盟高二下学期期中考试数学(理)试卷(已下线)《2018届优生-百日闯关系列》数学专题三 第四关 以解析几何中与圆相关的综合问题湖南省长沙市开福区长沙市第一中学2019-2020学年高二上学期第一次阶段性考试数学试题山东省滨州市博兴县2018-2019学年高二上学期期中数学试题西藏自治区拉萨中学2022届高三10月第二次月考数学(理)试题
2014高三·全国·专题练习
真题
名校
3 . 椭圆
的离心率
.
![](https://img.xkw.com/dksih/QBM/2014/4/12/1571617951850496/1571617957560320/STEM/9478a593-3437-4a39-aee4-bd5a8f98c33d.png?resizew=320)
(Ⅰ)求椭圆
的方程;
(Ⅱ)如图,
是椭圆
的顶点,
是椭圆
上除顶点外的任意一点,直线
交
轴于点
,直线
交
于点
,设
的斜率为
,
的斜率为
,试证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ee5043be616d5f554eae4f23670591.png)
![](https://img.xkw.com/dksih/QBM/2014/4/12/1571617951850496/1571617957560320/STEM/9478a593-3437-4a39-aee4-bd5a8f98c33d.png?resizew=320)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65183d238c9bc2be73770717d890683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9bf647642e5ee3f8b54f7de4926685.png)
您最近一年使用:0次
2016-12-02更新
|
2557次组卷
|
6卷引用:2013年普通高等学校招生全国统一考试文科数学(江西卷)
12-13高三下·江西·阶段练习
4 . 已知
是椭圆
和双曲线
的公共顶点.
是双曲线上的动点,
是椭圆上的动点(
、
都异于A、
),且满足
,其中
,设直线
、
、
、
的斜率分别记为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141c2cdc70061cfa9fb7283fd83047ec.png)
______________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49768c81dd7ffc82e4b1af2641be33ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d89edb09a343c23e415b3e7d8fd837b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c65902e35640cf2c8d4111c36b40145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2622fefdde380662d9e2ca07df2acfa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141c2cdc70061cfa9fb7283fd83047ec.png)
您最近一年使用:0次
13-14高二上·山东威海·期末
5 . 已知椭圆中心在原点,焦点在x轴上,离心率
,过椭圆的右焦点且垂直于长轴的弦长为![](https://img.xkw.com/dksih/QBM/2013/3/18/1571146844004352/1571146849820672/STEM/0ba977528af94efcb3fa44b843b24622.png?resizew=28)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)已知直线
与椭圆相交于
两点,且坐标原点
到直线
的距离为
,
的大小是否为定值?若是求出该定值,不是说明理由.
![](https://img.xkw.com/dksih/QBM/2013/3/18/1571146844004352/1571146849820672/STEM/9464a335bdc747b5b65c6b276de35dfb.png?resizew=52)
![](https://img.xkw.com/dksih/QBM/2013/3/18/1571146844004352/1571146849820672/STEM/0ba977528af94efcb3fa44b843b24622.png?resizew=28)
(Ⅰ)求椭圆的标准方程;
(Ⅱ)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
您最近一年使用:0次
2010·广东汕头·一模
名校
6 . 已知抛物线、椭圆和双曲线都经过点
,它们在
轴上有共同焦点,椭圆和双曲线的对称轴是坐标轴,抛物线的顶点为坐标原点
![](https://img.xkw.com/dksih/QBM/2010/6/27/1569774870986752/1569774876368896/STEM/dc604be322e54c4f977a9f5c8f36b499.png?resizew=274)
(1)求这三条曲线的方程;
(2)已知动直线
过点
,交抛物线于
两点,是否存在垂直于
轴的直线
被以
为直径的圆截得的弦
长为定值?若存在,求出
的方程,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2010/6/27/1569774870986752/1569774876368896/STEM/dc604be322e54c4f977a9f5c8f36b499.png?resizew=274)
(1)求这三条曲线的方程;
(2)已知动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521d2cbdff8483ebba708857163ef1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
长为定值?若存在,求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
您最近一年使用:0次
2012·福建龙岩·一模
7 . 以椭圆
:
的中心
为圆心,
为半径的圆称为该椭圆的“准圆”.设椭圆
的左顶点为
,左焦点为
,上顶点为
,且满足
,
.
(1)求椭圆
及其“准圆”的方程;
(2)若椭圆
的“准圆”的一条弦
(不与坐标轴垂直)与椭圆
交于
、
两点,试证明:当
时,试问弦
的长是否为定值,若是,求出该定值;若不是,请说明理由.
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/e94a837b8c9c449bbe0cdcde9a66d210.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/dc94d4377ce745799fee878dbbefd0f0.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/a665cfba064e40e6a66783f5d694a344.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/e4a162a17b81429fb812fd36de2d86c3.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/7c8e6aba340b4557afec35dd8271c2f5.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/47f2f923ef224082a8d04f73cae96b10.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/c581f24a8e514b4baf35d6959b5cf3d8.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/e1f4d8d2798d4f16acd5485c49b5456f.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/92ae6925733d484b87aab7e904af721a.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/3fc38808db444ca9a37b0d4119a30951.png)
(1)求椭圆
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/bcb3a0f4b06b4759aad40ef3dd79b943.png)
(2)若椭圆
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/7c8e6aba340b4557afec35dd8271c2f5.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/34fa18c9a9ec4e8da42abf0f046e019a.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/7c8e6aba340b4557afec35dd8271c2f5.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/34dc71127bb04f53be4793d64157d396.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/5b8f75b8901a49e29926354999b18d32.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/881fbd1ce77f4593bf13d2d7d76bad37.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040779763712/1573040785285120/STEM/728e7f242e254ee89546e8c1169f42fb.png)
您最近一年使用:0次
2016-12-01更新
|
876次组卷
|
3卷引用:2015-2016学年江西省于都三中高二第三次月考理科数学试卷
2012·福建福州·一模
名校
8 . 如图,圆
与
轴相切于点
,与
轴正半轴相交于
两点(点
在点
的下方),且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/9f1e1599-2835-4ff8-ad46-aed81e934d71.png?resizew=167)
(1)求圆
的方程;
(2)过点
任作一条直线与椭圆
相交于两点
,连接
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6614916203fe0146d6797138da3db4a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc5931d25e50c27e61e78347f9370e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/9f1e1599-2835-4ff8-ad46-aed81e934d71.png?resizew=167)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729cf1d18cbb0ff509b51be7c445c34e.png)
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9 . 线段
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