名校
解题方法
1 . 已知椭圆
,四个点
,
,
,
中恰有三点在椭圆C上.
(1)求椭圆C的方程;
(2)设直线
与椭圆C相交于A,B两点.若直线
与直线
的斜率的和为
,判断直线l是否经过定点,若过定点,求出定点坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f669a1d6376f795f05b47eb7d8067c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fbf46db1c38fdcefdfca8777a92875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea67de74c0d7a7c48df4329a625e9234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662c8324ff4c288337a2dbf78be863b4.png)
(1)求椭圆C的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e9f87f36df625060ebf7b0ede71b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3de68627f7f3d7f81b61bf743f311ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9019a986b3ba5fcefced99c566b5329c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
您最近一年使用:0次
2023-02-22更新
|
383次组卷
|
3卷引用:江西省南昌市第十九中学2022-2023学年高二下学期第一次(3月)月考数学试题
名校
解题方法
2 . 已知椭圆C:
的离心率为
,以椭圆的四个顶点为顶点的四边形周长为
.
(1)求椭圆的方程;
(2)直线
与椭圆
交于
、
两点,与
轴交于点
,线段
的垂直平分线与
交于点
,与
轴交于点
,
为坐标原点,如果
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588c3822b7812e711b4ad86647b15dc1.png)
(1)求椭圆的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/906d113790775f98626dbabc341ceaee.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eaf5d0136690877162121e795f13724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-02-07更新
|
2650次组卷
|
14卷引用:江西省上高二中2022-2023学年高二下学期4月月考数学试题
江西省上高二中2022-2023学年高二下学期4月月考数学试题北京市西城区2022届高三一模数学试题吉林省洮南市第一中学2022届高三下学期第一次线上考试数学(理)试题北京市清华大学附属中学朝阳学校2021-2022学年高二5月月考数学试题天津市第四十七中学2022届高三下学期四月统练数学试题北京市海淀区第二十中学2023届高三上学期12月月考数学试题湖南省常德市临澧县第一中学2022-2023学年高二下学期入学考试数学试题安徽省阜阳市第二中学2023届高三下学期第一次月考数学试题北京市陈经纶中学2023届高三下学期综合练习一(开学考试)数学试题北京市海淀区2023届高三一模数学试题查漏补缺练习天津市南开中学2024届高三上学期统练2数学试题(已下线)专题10 圆锥曲线综合大题10种题型归类-【寒假分层作业】2024年高二数学寒假培优练(人教A版2019选择性必修第一册)广东省信宜市某校2023-2024学年高二下学期开学考试数学试题四川省绵阳南山中学实验学校2024届高三下学期4月月考理科数学试题
3 . 已知椭圆C:
的左、右顶点分别为A,B,右焦点为F,折线
与C交于M,N两点.
(1)当m=2时,求
的值;
(2)直线AM与BN交于点P,证明:点P在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640bcaecb7b575307c199d828ba96384.png)
(1)当m=2时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3adfb8ef95245d7d073de76ceb053a.png)
(2)直线AM与BN交于点P,证明:点P在定直线上.
您最近一年使用:0次
2023-02-01更新
|
481次组卷
|
3卷引用:江西省宜春市宜丰县宜丰中学2023届高三上学期期末数学试题
解题方法
4 . 已知椭圆
:
的左右焦点分别为
,
,右顶点为
,上顶点为
,
为坐标原点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1813c35af72db0e4270851643f0046a7.png)
(1)若
的面积为
,求椭圆
的标准方程:
(2)过点
作斜率
的直线
交椭圆
于不同两点
,
,点
在椭圆的内部,在椭圆上存在点
,使
,记四边形
的面积为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/a3fb78c5f885034612c0e030b920143d.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1813c35af72db0e4270851643f0046a7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bdac20e214b2cb3bd07f8d4778dcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33596942b30bd702100223fcdddbad7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe3174b77e624cd0fdb730bbe00322f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1771faca0c78edf5c2d5485718e1db.png)
您最近一年使用:0次
名校
解题方法
5 . 已知椭圆
的左焦点为
,右焦点为
,离心率
,过
的直线交椭圆于P,Q两点,且
的周长为8.
(1)求椭圆E的方程;
(2)已知过点
与椭圆E相切的直线分别为
,直线
与椭圆E相交于A,B两点,与
分别交于点M,N,若
,求t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.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/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fea5f7430235e65d2c2e6b2ecc46712.png)
(1)求椭圆E的方程;
(2)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdbb3816e8ab1e2ebe3453cfeb1598a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4147f37263dc5cdebcf9d53b758977dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70be3e941a4ce0f82ed61790c61a22fd.png)
您最近一年使用:0次
2023-01-09更新
|
243次组卷
|
3卷引用:江西省南昌市第十中学2022-2023学年高二下学期第一次月考数学试题
6 . 已知双曲线
:
的离心率为
,其左、右顶点分别为
,
,右焦点为
,
为
的左支上不同于
的动点,当
的纵坐标为
时,线段
的中点恰好在
轴上.
(1)求双曲线
的标准方程;
(2)若点
,连接
交
的右支于点
,直线
与直线
相交于点
,证明:当
在
的左支上运动时,点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f387b16cc48e57112c89c8af2a90c1d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
解题方法
7 . 已知椭圆
的离心率为
,以原点为圆心、椭圆的短半轴长为半径的
与直线
相切.
(1)求椭圆
的方程;
(2)过定点
斜率为
的直线与椭圆
交于
两点,若
,求实数
的值及
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5ab74296abcbcf994c02b5834cd699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38f9106cef0b638e62c90afc1c523cd.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451fc6e4248b63e70595f23842f06c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/e2ebbb89a7c50ed23e32f1dcad606c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
您最近一年使用:0次
2023-01-07更新
|
523次组卷
|
5卷引用:江西省宜春市丰城第九中学2023届高二下学期(重点28、29班)开学质量检测数学试题
23-24高三上·湖南永州·阶段练习
名校
解题方法
8 . 已知
为坐标原点,椭圆
的左、右焦点分别为
,直线
与椭圆
交于
两点,当
的周长取得最大值8时,
.
(1)求椭圆
的标准方程;
(2)过点
作斜率存在且不为0的直线
交椭圆
于
两点,若
,直线
与直线
交于点
,记直线
的斜率分别为
,试判断
是否为定值,若是,求出该定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/a1be7302f2e9ff02fee3fcf26e77b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571b23af766b48bdd93fc228ca9c7860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3492aa2ed6ee3b586343969821832881.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9adacbefdb2a988cc6e0d92a51bbe8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3fbcd952073f38340769b8fbca5b23.png)
您最近一年使用:0次
名校
解题方法
9 . 已知椭圆
,倾斜角为
的直线过椭圆的左焦点
和上顶点B,且
(其中A为右顶点).
(1)求椭圆C的标准方程;
(2)若过点
的直线l与椭圆C交于不同的两点P,Q,且
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e2c8fa12344e36efba94ab6f6df05d.png)
(1)求椭圆C的标准方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d3175ab92b729dfd24f209e448e600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3de67f64270935ceb31a169d5c8a84.png)
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2022-12-17更新
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8卷引用:江西省南昌市三校(一中、十中、铁一中)2023届高三上学期第二次联考数学(理)试题
江西省南昌市三校(一中、十中、铁一中)2023届高三上学期第二次联考数学(理)试题广西南宁市第二中学2023届高三上学期第一次综合质检数学(文)试题湖北省武汉市第六中学2022-2023学年高二上学期第三次月考数学试题(已下线)专题13 圆锥曲线压轴解答题常考套路归类(精讲精练)-1(已下线)山东省济南市2022届高三二模数学试题变式题17-22甘肃省兰州市西固区兰州市第六十一中学2023届高三上学期期末理科数学试题陕西省西安市铁一中学2023-2024学年高三上学期第二次月考理科数学试题(已下线)陕西省西安市铁一中学2023-2024学年高三上学期第二次月考理科数学试题变式题19-22
10 . 已知椭圆
的标准方程为
.
(1)求椭圆
被直线
截得的弦长;
(2)若直线
与椭圆交于
,
两点,当
(O为坐标原点)时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.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/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-12-15更新
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2卷引用:江西省临川第二中学2022-2023学年高二上学期第三次月考数学试题