名校
解题方法
1 . 已知椭圆C:
的左、右焦点分别为
,
、
,
,点
在椭圆C上.
(1)求椭圆C的方程;
(2)过点
的动直线l与椭圆C交于不同的两点A,B.试问x轴上是否存在定点Q,使得x轴恰好平分
?若存在,求出定点Q的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768fef914945a6e28f1f41740951435c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1151e47dfad2fc7e7dff6ebc17f7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850807898e7f29cb655608441af4064d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58e766e83bea5517ea54065165fe60a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850807898e7f29cb655608441af4064d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b550e4f9cee5d018ceffe7c0eaab8405.png)
(1)求椭圆C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8387b687579c4d5152175c9d19e24232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c7bbe0ac1c88c9d35978a7184ba553.png)
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解题方法
2 .
,
分别是椭圆
的左右焦点,B是椭圆的上顶点,过点
作
的垂线交椭圆C于P,Q两点,若
,则椭圆的离心率是( )
![](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/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2a7edc2f69ef37fd14a446f9b16b8e.png)
A.![]() ![]() | B.![]() ![]() | C.![]() | D.![]() |
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2024-02-21更新
|
145次组卷
|
2卷引用:理科数学-【名校面对面】2022-2023学年高三大联考(2月)试题
解题方法
3 . 已知椭圆
的离心率为
.直线
经过点
和椭圆
的上顶点,其斜率为
.
的标准方程;
(2)若直线
与椭圆
交于
、
两点,直线
与椭圆
的另一个交点为
,直线
与椭圆
的另一个交点为
.求证:当
变化时,直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf02334810fe35d00fe99d2945fbfbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861fe213ebc09184f67a05173ad3a941.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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解题方法
4 . 已知椭圆
的左、右焦点分别为
是椭圆
的上顶点,线段
的延长线交椭圆
于点
.若
,则椭圆
的离心率
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c893bc5081ac0a24d4b112982d26d793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.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/9a76408ed2eec84790040ac61fa1b540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ce2b47812fce4b17fd813d0e4cce21.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知椭圆
:
的离心率为
,且过点
,点
与点
关于原点对称,过点
作直线l与E交于
,
两点(异于
点),设直线
与
的斜率分别为
,
.
(1)若直线l的斜率为
,求
的面积;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16bd471deb1d369d93951a7b1af07b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8902bff3e60ecebdcd71bb2ee8bb97b.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/5963abe8f421bd99a2aaa94831a951e9.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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(1)若直线l的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86696ba6c5cd670ab8b9dcbd4fb63bb.png)
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2024-02-12更新
|
491次组卷
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3卷引用: 上海市实验学校2023-2024学年高三3月数学练习试卷
6 . 在平面直角坐标系xOy中,已知椭圆C:
,斜率为
且不过原点的直线l交椭圆C于A,B两点,线段AB的中点为E,射线OE交椭圆C于点G,交直线
于点
.若
.求证:直线l过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc603fea876cbf85b1efcb5bab0d500f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bdac20e214b2cb3bd07f8d4778dcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093836f9680ca10fdedd509558a04836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88f44df62b3a77b0a440efeec41e615.png)
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名校
解题方法
7 . 已知椭圆
,
是椭圆
的一条弦
的中点,点
在直线
上,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0a931aad97bb54ad7017c277f4210e.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/fbf1a8f59377d4cc5f3197ebcb52c3d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024高二上·全国·专题练习
8 . 已知直线
与椭圆
.
(1)若它们有两个公共点,求
的取值范围;
(2)若它们只有一个公共点,求公共点的横坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
(1)若它们有两个公共点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若它们只有一个公共点,求公共点的横坐标.
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名校
解题方法
9 . 已知椭圆
的左、右焦点分别为
,上、下顶点分别为
,四边形
的面积为
,且
.
(1)求椭圆
的标准方程;
(2)过点
的直线
与椭圆
交于
两点,连接
,若直线
的一个方向向量为
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34c0b2434f080f2187a1722f3c00b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887e6a708586e18b1aa8690ad40f7036.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbaa023d0248161917794c5592fd3a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
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3卷引用:第7讲:圆锥曲线的模型【练】
10 . 已知动点M到点
的距离与到直线l:
的距离之比等于
.
(1)求动点M的轨迹W的方程;
(2)过直线l上的一点P作轨迹W的两条切线,切点分别为A,B,且
,
①求点P的坐标;
②求
的角平分线与x轴交点Q的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7422cbdb4ad06d155abb2ccdb25ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求动点M的轨迹W的方程;
(2)过直线l上的一点P作轨迹W的两条切线,切点分别为A,B,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15b82151bff7cc0238d2034a6129f0.png)
①求点P的坐标;
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
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