解题方法
1 . 已知椭圆
的右顶点为
,离心率为
.
(1)求椭圆
的方程;
(2)过点
的直线
与椭圆
交于另一点
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3838b4bedea24f8a0bb9883642e441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-03-10更新
|
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3卷引用:湖南省三湘创新发展联合体2023-2024学年高三下学期2月开学统试数学试题
名校
解题方法
2 . 已知椭圆
:
(
)经过点
,
.
(1)求椭圆
的标准方程;
(2)已知点
,
,
为椭圆
上异于A的两点,且
,证明:直线
过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cda9ce6d633bc1f3a249fb0fc458a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303e6de91a36b8ca92ae42c952cad8af.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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2024-02-23更新
|
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2卷引用:湖南省永州市第一中学2023-2024学年高二下学期开学检测数学试题
名校
解题方法
3 . 已知分别为椭圆
的左,右顶点,
为其右焦点,
,且点
在椭圆
上.
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba6af95c79e80c772653374c05c21f3.png)
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2023-05-07更新
|
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9卷引用:湖南省长沙市明德中学2023-2024学年高三上学期入学考试数学试题
湖南省长沙市明德中学2023-2024学年高三上学期入学考试数学试题广西桂林市、北海市2023届高三联合模拟考试数学(理)试题海南省琼海市2023届高三模拟考试数学试题四川省成都市双流区永安中学2022-2023学年高二下学期零模模拟考试数学试题(已下线)第02讲 3.1.2椭圆的简单几何性质(2)(已下线)第08讲 直线与圆锥曲线的位置关系(练习)江西省丰城中学2023-2024学年高一上学期12月月考数学试题(已下线)第04讲 拓展一:直线与椭圆的位置关系-【练透核心考点】2023-2024学年高二数学上学期重点题型方法与技巧(人教A版2019选择性必修第一册)(已下线)云南省昆明市2024届高三“三诊一模”摸底诊断测试数学试题变式题17-22
名校
4 . 已知椭圆
,
、
两点分别为椭圆的左顶点、下顶点,
是椭圆的右焦点,
,直线
与椭圆相切与
(
在第一象限),与
轴相交于
(
异于
),记
为坐标原点,若
是等边三角形,且
的面积为
,
(1)求椭圆的标准方程;
(2)
、
两点均在直线
:
,且
在第一象限,设直线
、
分别交椭圆于点
,点
,若
、
关于原点对称,求
的最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ec88afee8628dae6ce0eb999267c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆的标准方程;
(2)
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316699c45f1c088945d0cd3bb46eecfb.png)
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2023-02-10更新
|
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3卷引用:湖南省株洲市第二中学2023-2024学年高三下学期开学考试数学试卷
5 . 已知椭圆
的左右焦点分别为
,椭圆C经过点
,且直线
,与圆
相切.
(1)求椭圆C的方程;
(2)直线
与椭圆C交于P,Q两点,点M在x轴上,且满足
,求点M横坐标的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
(1)求椭圆C的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53cd24fdb222c2e68c05c21600383df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db64a7467f0abcfe06cc9b279a5be7c.png)
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2023-02-03更新
|
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|
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2022·全国·模拟预测
名校
6 . 如图所示,平面直角坐标系
中,四边形
满足
,
,
,若点
,
分别为椭圆
:
(
)的上、下顶点,点
在椭圆
上,点
不在椭圆
上,则椭圆
的焦距为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd99a6862833b220a7371852a3570bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2f21563f519fc8c47288b2b020e63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521d0d12d0e06969e58f56899ea3cd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171b08c1122ed5d395dc72e9a8ee1390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289d7a880379d6060065c829b45b0ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/3630d768-f176-4123-8f79-2f6d1f90d5b0.png?resizew=137)
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2022-12-05更新
|
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|
5卷引用:湖南省株洲市第二中学2022-2023学年高二下学期入学考试数学试题
名校
解题方法
7 . 在平面直角坐标系中,已知椭圆
的左、右顶点分别为A、B,右焦点F,且椭圆
过点
、
,过点F的直线l与椭圆
交于P、Q两点(点P在x轴的上方).
的标准方程;
(2)设直线AP、BQ的斜率分别为
、
,是否存在常数
,使得
?若存在,请求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62645f10a184693406c85b90386b43d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67994a247ab680cdb0e64d8f943ca7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f3ec4e60834ee438d3f44355e76650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)设直线AP、BQ的斜率分别为
![](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/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3486e73c205299afe93b217ac848b3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2022-04-04更新
|
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4卷引用:湖南省岳阳市平江县颐华高级中学2024届高三下学期入学考试数学试题
名校
解题方法
8 . 已知椭圆C:
(
)的短轴长为
,P(
,1)是椭圆C上一点.
(1)求椭圆C的方程;
(2)过点M(m,0)(m为常数,且
)的直线l与椭圆C交于不同的两点A,B,与y轴相交于点N,已知
,
,试问
是否为定值?若是、请求出该值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求椭圆C的方程;
(2)过点M(m,0)(m为常数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be17a78f969ea0ce201d42bb0485dc43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5652e94063be35668450ec2f44347a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb6303671277c3091f0e787c59cdbdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cadde34eff805eb41c5c1cbe75f62a.png)
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2022-03-14更新
|
339次组卷
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4卷引用:湖南省百所学校大联考2021-2022学年高二下学期入学考试数学试题
湖南省百所学校大联考2021-2022学年高二下学期入学考试数学试题(已下线)湖南省长沙市长郡中学2022届高三下学期月考(六)数学试题广东省广州市铁一等三校2021-2022学年高二下学期期中联考数学试题上海市建平中学2023-2024学年高二上学期期中数学试题
名校
解题方法
9 . 已知椭圆C:
(a>b>0),点P(1,
)在椭圆上,且离心率e=
.
(1)求椭圆C的方程;
(2)若椭圆C的右焦点为F,过B(4,0)的直线l与椭圆C交于D,E两点,求证:直线FD与直线FE斜率之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆C的方程;
(2)若椭圆C的右焦点为F,过B(4,0)的直线l与椭圆C交于D,E两点,求证:直线FD与直线FE斜率之和为定值.
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2022-03-14更新
|
520次组卷
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