名校
解题方法
1 . 如图,已知椭圆
,其焦距为4,过椭圆长轴上一动点
作直线交椭圆于
、
,直线
、
交于点
,已知
,则椭圆的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715abe79425e4e4f2a35fdd745ba653b.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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468fc3e395fa3b681c3da37edbe229a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25ec7f5d958d54f9642eecec56e7540.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/f78746a7-c640-4a95-b14e-790feb628e1b.png?resizew=189)
您最近一年使用:0次
2024-01-11更新
|
287次组卷
|
2卷引用:湖北省武汉市东湖中学2023-2024学年高二上学期期中考试数学试题
2022高三·全国·专题练习
解题方法
2 . 已知
,
,
为曲线
的左、右焦点,点
为曲线
与曲线
在第一象限的交点,直线
为曲线
在点P处的切线,若三角形
的内心为点M,直线
与直线
交于N点,则点
横坐标之差为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce64fa0d35183e9cea4b93bef8b53fe1.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/4dfd67a867ed71a09f95446d45a26b2d.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/e6ff52816bf2fc5d975a368e8856898f.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/cf8a7029669bf1774a24f3ef6273ca88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8ad9e94d07405a6be585f81a0d623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
您最近一年使用:0次
2023-11-30更新
|
571次组卷
|
7卷引用:江西省部分学校2024届高三上学期期中数学试题
江西省部分学校2024届高三上学期期中数学试题(已下线)专题8 求定点定值运算(提升版)(已下线)3.3(附加3)圆锥曲线定点与定值问题-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)考点20 常用的二级结论的应用 2024届高考数学考点总动员【练】(已下线)专题03 圆锥曲线方程(3)(已下线)大招11焦点三角形的内心(已下线)专题8 圆锥曲线与三角形四心问题【练】(压轴小题大全)
解题方法
3 . 已知椭圆
与抛物线
交于点
,直线
与
轴的交点既是
的右焦点,也是
的焦点,点
关于原点的对称点分别为
,点
是
上与
均不重合的点,记直线
的斜率分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4762ec251b2d6749024ae68f74e9a650.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0107aa23cf707446f947fa236421c1f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77993759b8615ef0b42cb56ef027ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4dfc408125cc3d651bc9123abd77ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b5f5621f4805a499c715f4f7cc6f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d8707cafd80cde5c561e2b5a3531c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4762ec251b2d6749024ae68f74e9a650.png)
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4 . 已知O为坐标原点,设
分别是椭圆
的左、右焦点,点P为椭圆上任一点,过点
作
的外角平分线的垂线,垂足为H,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a21c7238d25c832d3dffd6cd0b289a2.png)
____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde88bfd7d2406b3ffcd38e99a39b1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff77d03dd8da9a13d1870b95602d492b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2aaa7aba7f01975f54721e86c6f86b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a21c7238d25c832d3dffd6cd0b289a2.png)
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5 . 已知椭圆
满足
,长轴
上2023个等分点从左至右依次为点
,过点
作斜率为
的直线,交椭圆于
两点,
点在
轴上方;过
点作斜率为
的直线,交椭圆于
两点,
点在
轴上方;以此类推,过
点作斜率为
的直线,交椭圆于
两点,
点在
轴上方;则这4046条直线
的斜率乘积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4037561c629fd07503c6803e1eb62fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a966c052bf174f1edb202f587df658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1361a10d0d1973969bec5e537c518a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea22b9539f9e6f0ebb43b9d433fad91c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd873c4de5c5bd9ed419889416b993e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6392cab26ba6aec9391bf56787eae05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d03d03aa575c6dbb34aa79591ee8740.png)
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名校
解题方法
6 . 已知椭圆
的离心率为
,点
为其长轴两端点,点
为椭圆
上异于
的一点,则直线
和
的斜率之积等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2103f44b9f6bc9e7db92b92bfaa87f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.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/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
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名校
7 . 椭圆
的弦
满足
,记坐标原点
在
的射影为
,则到直线
的距离为1的点
的个数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e09263551bca1d9256295c822a9faa75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc11e7549cfce9220e70250ac943e457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2023-11-11更新
|
454次组卷
|
3卷引用:江苏省常州市第一中学2023-2024学年高二上学期11月期中数学试题
8 . 已知点
满足方程
,点
,
,若直线
的斜率为
,
斜率为
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82d78bf82a5e70a3761b83935735ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b7724704df2f30fbcf31fc86a7daee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
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名校
9 . 如图,在平面直角坐标系
中,
,
分别为椭圆
的左,右焦点,
、
分别为椭圆的上、下顶点,直线
与椭圆的另一交点为
,若
,则直线
的斜率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/48da128547c4cf9745e8e4b99988a3db.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/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0eff213692434b15d51cdf40f497e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/3c909fea-07fb-410e-b42a-7c64b337b05d.png?resizew=181)
您最近一年使用:0次
2023-07-09更新
|
528次组卷
|
4卷引用:浙江省诸暨中学暨阳分校2023-2024学年高二上学期期中考试数学试题
10 . 已知点M、N分别是椭圆
上两动点,且直线
的斜率的乘积为
,若椭圆上任一点P满足
,则
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091145fcc157587a3fc8e0b7c7c0ecb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9909ded4aa86b799e374c53a11a3c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c07b101a1a118c7558a9e59b13c95c.png)
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