名校
解题方法
1 . 已知抛物线
,O是坐标原点,过
的直线与E相交于A,B两点,满足
.
(1)求抛物线E的方程;
(2)若
在抛物线E上,过
的直线交抛物线E于M,N两点,直线
,
的斜率都存在,分别记为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c42d88e496a17562d25195301e0ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(1)求抛物线E的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c261201283d56c071c1c8133dc20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b72de4221a7de45fad497d0bb7ac1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.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/6b881044b5c73db6fcce110525741b02.png)
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2024-04-10更新
|
1063次组卷
|
3卷引用:广西南宁市第二中学·柳州高级中学2023-2024学年高二下学期5月联考数学试题
解题方法
2 . 以椭圆
的长轴端点为焦点、以椭圆焦点为顶点的双曲线方程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
您最近一年使用:0次
3 . 已知A,B为抛物线C:
上的两点,△OAB是边长为
的等边三角形,其中O为坐标原点.
(1)求C的方程.
(2)过C的焦点F作圆M:
的两条切线
,
.
(i)证明:
,
的斜率之积为定值.
(ii)若
,
与C分别交于点D,E和H,G,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6d8eaacc2d999b37209feba103f9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6093eebca8f3ff82ce9298feb197e955.png)
(1)求C的方程.
(2)过C的焦点F作圆M:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15fc1af2a824c1f6a0aa4618e5e6dfa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f160e6da63385867807453959174f41.png)
您最近一年使用:0次
名校
4 . 椭圆的上顶点到双曲线
的渐近线的距离为( )
A.![]() | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
2024-03-24更新
|
717次组卷
|
2卷引用:广西百所名校2023-2024学年高二下学期入学联合检测数学试题
名校
解题方法
5 . 过双曲线
的左焦点
作圆
的切线,切点为
,直线
交直线
于点
.若
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4be819fc47b2aa19ab2022b3dfeb6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5073552dadf6b05b65dabb17aef220a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a36a98bea677dd30b758403a95c4d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-21更新
|
1710次组卷
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4卷引用:广西南宁市第二中学2023-2024学年高二下学期期中考试数学试卷
广西南宁市第二中学2023-2024学年高二下学期期中考试数学试卷2024届天津市十二区县重点学校一模模拟考试数学试卷(已下线)第1题 双曲线的离心率问题(5月)(压轴小题)(已下线)【人教A版(2019)】高一下学期期末模拟测试A卷
6 . 抛物线
的准线方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04441cb6f7439879a136565607d31337.png)
您最近一年使用:0次
解题方法
7 . 已知
,
分别是椭圆M:
的左、右焦点,点P在椭圆M上,且
,则M的离心率可能为( )
![](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/52c2ba356b73210d99f0e11afdb2bb04.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 已知椭圆
的离心率为
,且椭圆
的短轴长为
.
(1)求椭圆
的方程.
(2)设
是椭圆
上第一象限内的一点,
是椭圆
的左顶点,
是椭圆
的上顶点,直线
与
轴相交于点
,直线
与
轴相交于点
.记
的面积为
,
的面积为
.证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59c4295f918205f5598ecc9a96d8867.png)
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2024-03-11更新
|
654次组卷
|
5卷引用:广西壮族自治区桂林市2023-2024学年高二下学期入学联合检测卷数学试题
解题方法
9 . 已知点
,动点
满足
,记点
的轨迹为曲线
.
(1)求
的方程;
(2)若
是
上不同的两点,且直线
的斜率为5,线段
的中点为
,证明:点
在直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b10869dee07ab7948bfdb81ad58f134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1350897d718a2592dfe8f8ddc5154e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7f8878d628d46bcb847f791857b650.png)
您最近一年使用:0次
2024-03-10更新
|
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2卷引用:广西百所名校2023-2024学年高二下学期入学联合检测数学试题
10 . 已知抛物线
的焦点为
,
是
上一点,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd29b2e8192d673308bdf8d5cb6cab.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6988a98f2a07be492b6b7df1bccc7480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bab7f5ed5e6578879a7bbd02e60263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd29b2e8192d673308bdf8d5cb6cab.png)
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2024-03-10更新
|
464次组卷
|
5卷引用:广西壮族自治区桂林市2023-2024学年高二下学期入学联合检测卷数学试题