1 . 已知椭圆
的离心率为
,且过点
.过椭圆
上的点
作圆
的两条切线,其中一条切线与椭圆
相交于点
,与圆
相切于点
,两条切线与
轴分别交于
两点.
的方程;
(2)
是否为定值,若是,请求出
的值;若不是,请说明理由:
(3)若椭圆上点
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90627d25fa0d0e5345c834b96331e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959e5ab675f526dfb54b05f8f82151b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2228629b80d4efbfd2a226a863274520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2228629b80d4efbfd2a226a863274520.png)
(3)若椭圆上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c81a4d934b8e4565969a8e7921111c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
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2 . 已知椭圆C:
过点
,直线
与椭圆
交于
两点,且线段
的中点为
为坐标原点,直线
的斜率为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a1baa2dbbdb3bca1776d10b288cd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73533688e2820dacba2199ba6087bd4e.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876f208635a511c8dc89da1dad21c868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
A.![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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名校
解题方法
3 . 已知点
是圆
的动点,过
作
轴,
为垂足,且
,
,记动点
,
的轨迹分别为
,
.
(1)证明:
,
有相同的离心率;
(2)若直线
与曲线
交于
,
,与曲线
交于
,
,与圆
交于
,
,当
时,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efd7b690113cfc851401e1540ac1132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb8f6c438fe1fc036c92ccd3fa8465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5d3e8de22b4cadd3aacc6b955dbcd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b62adcc036ff4122e642b506d46c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6824ebd7ee7da0bed69bd761dbb762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.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/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/457e56d8aa132b2aad38ecf7e45f1cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34d2c05dd46ab2ac99d32be44a1465c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3c6876c328f7d7a08515e78fdba136.png)
您最近一年使用:0次
2024-02-28更新
|
349次组卷
|
2卷引用:浙江省金华市2023-2024学年高三上学期2月期末考试数学试题
名校
解题方法
4 . 已知椭圆
的离心率为
,左、右焦点分别为
,
,点P为椭圆C上任意一点,
面积最大值为
.
(1)求椭圆C的方程;
(2)过x轴上一点
的直线与椭圆交于A,B两点,过A,B分别作直线
的垂线,垂足为M,N两点,证明:直线
,
交于一定点,并求出该定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆C的方程;
(2)过x轴上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724e11601d3807c120713018d3405d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
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解题方法
5 . 已知椭圆
的离心率为
,椭圆
上的点与点
的距离的最大值为4.
(1)求
的方程;
(2)设
轴上的一定点
,过点
作直线
交椭圆
于
,
两点,若在
上存在一点A,使得直线
的斜率与直线
的斜率之和为定值,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d059a0d71bddb677c603d84fac444b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439e95540157803d4ac3cf61a49f50a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
6 . 已知椭圆
的短轴长为2,且离心率为
.
(1)求椭圆
的方程;
(2)设椭圆
的上、下顶点分别为点
,过点
的直线
与椭圆
交于不同两点
,且
,直线
与直线
交于点
,求证:点
在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ed90ebf0061c8a79beed307fc1719a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1325c6fe42a9e5c04520d8a9bb6821b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f99df1a7b58018125b99578b779342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
7 . 已知椭圆
,
,
分别是椭圆C的左、右焦点,点
为左顶点,椭圆上的点到左焦点距离的最小值是焦距的
.
(1)求椭圆
的离心率;
(2)直线
过椭圆C的右焦点
,与椭圆C交于P,O两点(点P在第一象限).且
面积的最大值为
,
①求椭圆C的方程;
②若直线
,
分别与直线
交于
,
两点,求证:以
为直径的圆恒过右焦点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd3b3e802743d1c239c192c7fb8a599.png)
①求椭圆C的方程;
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c716601286ac3ef51a4c3c16b12e260.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
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名校
8 . 已知椭圆
,双曲线
(
,
),椭圆
与双曲线
有共同的焦点,离心率分别为
,
,椭圆
与双曲线
在第一象限的交点为
且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8210484dd6815b5bebc7b22f1389cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ab2caccd742eb636bd8378661a8807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b967232e28ad0d453adc66676bdf8b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f1ea30341eb5d584710c3aebc64ce8.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/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7285470bf401f5edaac641234ee6ff6a.png)
A.若![]() ![]() |
B.![]() ![]() |
C.![]() ![]() ![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-01-15更新
|
550次组卷
|
5卷引用:辽宁省葫芦岛市2023-2024学年高二上学期1月普通高中学业质量监测考试数学试题
名校
解题方法
9 . 已知椭圆
的离心率为
,右焦点与抛物线
的焦点重合,上顶点B到直线
的距离为
.
(1)求椭圆
和抛物线
的标准方程;
(2)若直线
与椭圆
交于H,K两点,与抛物线
交于M,N两点,过点M作x轴的垂线,与直线
交于点G,点M关于点G的对称点为P,且O,N,P三点共线,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0107aa23cf707446f947fa236421c1f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c7a9ead1792edf06a0f7bdb2064317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af46665388a510b902827786edffaf8d.png)
您最近一年使用:0次
2024-01-06更新
|
748次组卷
|
2卷引用:广东省珠海市第一中学2024届高三上学期大湾区期末数学预测卷(三)
10 . 已知椭圆
的两焦点分别为
的离心率为
上有三点
,直线
分别过
的周长为8.
(1)求
的方程;
(2)①若
,求
的面积;
②证明:当
面积最大时,
必定经过
的某个顶点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704bfc280d817fb77006ee98d4d7e5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99276d856410431e6ed0b59fc27e5264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c8c8746a97d79afa729753ef8b38ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2304324f76e8efaaec4fa0c6b677879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdba598caa59b8a2a68f6aed5de15525.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28c23cfc5eb8416cdf74c2da06e5656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffd5d363ebeaa6de0ff830742643db4.png)
②证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffd5d363ebeaa6de0ff830742643db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffd5d363ebeaa6de0ff830742643db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2023-12-17更新
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4卷引用:模块六 全真模拟篇 拔高1 期末终极研习室(2023-2024学年第一学期)高三
(已下线)模块六 全真模拟篇 拔高1 期末终极研习室(2023-2024学年第一学期)高三福建省厦门第一中学2023-2024学年高二上学期十二月月考数学试卷江苏省扬州市扬州中学2024届新高考一卷数学模拟测试一福建省泉州市实验中学2023-2024学年高二上学期12月月考数学试题