1 . 已知椭圆
的离心率为
,
(1)若原点到直线
的距离为
,求椭圆的方程;
(2)设过椭圆的右焦点且倾斜角为
的直线
和椭圆交于
、
两点,
①当
时,求
的值;
②对于椭圆上任一点
,若
,求实数
、
满足的关系式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1030e95e6804c2bde40425b036029663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)若原点到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5e9b42db47cab2520cd32c09b47d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(2)设过椭圆的右焦点且倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19efd2f2662ca444c784b69e35f53120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
②对于椭圆上任一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a24fbe4755454d01b7168a93b26018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,已知椭圆
的左、右焦点分别为
,过椭圆左焦点
的直线与椭圆
相交于
两点,
,
,则椭圆
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c388f94adc940de0fd317d00b3cd9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040b10c7d1c56f08e3d31a61195c689a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/a1e3ab5b-2a04-417e-aeee-b7ba4905e233.png?resizew=165)
您最近一年使用:0次
2024-01-25更新
|
322次组卷
|
5卷引用:甘肃省庆阳市环县第一中学2023-2024学年高二上学期期末考试数学试题
3 . 已知
为椭圆
的右焦点,离心率为
.
(1)求
的方程;
(2)若
是平面上的动点,直线
不与坐标轴垂直,从下面两个条件中选择一个,证明:直线
经过定点.
①
为椭圆
上两个动点,且
;
②
为椭圆
上两个动点,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b406c5e06b7790b2e481a8ce3f5e33c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3551efb72b95def8f1877b5c38d71192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a877428408d09ac0112f833e54a8e34a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282298a866831ea4a8cdf96ae28c0aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a877428408d09ac0112f833e54a8e34a.png)
您最近一年使用:0次
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解题方法
4 . 已知椭圆
的离心率为
是
上一点.
(1)求椭圆
的方程.
(2)
是
的右顶点,过点
的直线
与
相交于
两点(异于点
),直线
的斜率分别
,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/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c08f3b04f08324a112ea1bca6cad3bf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](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/af74113f38fffeed8075e57d7f9d2533.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d42cb68c5c877a455ba7ac0a6b6a651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
2023-11-25更新
|
387次组卷
|
3卷引用:甘肃省兰州第一中学2023-2024学年高二上学期1月期末数学试题
名校
解题方法
5 . 已知
,
是椭圆
的左右顶点,
是双曲线
在第一象限上的一点,直线
,
分别交椭圆于另外的点
,
.若直线
过椭圆的右焦点
,且
,则椭圆的离心率为________ .
![](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/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b3ebb0c18ca94b7728f3e965859082.png)
您最近一年使用:0次
2023-10-19更新
|
1241次组卷
|
6卷引用:甘肃省兰州市第五十八中学2023-2024学年高二上学期期末数学试题
甘肃省兰州市第五十八中学2023-2024学年高二上学期期末数学试题江苏省南京师范大学附属中学2023-2024学年高三上学期期末模拟数学试题湖北省腾云联盟2023-2024学年高三上学期10月联考数学试题湖北省武汉市部分高中2023-2024学年高三上学期10月联考数学试题江苏省盐城市射阳县射阳中学2023-2024学年高二上学期期中数学试题(已下线)高二数学上学期期中考模拟卷(直线与方程+圆与方程+圆锥曲线与方程)-【考点通关】2023-2024学年高二数学高频考点与解题策略(苏教版2019选择性必修第一册)
解题方法
6 . 已知椭圆
:
的离心率为
,左、右焦点分别为
,
,左、上顶点分别为
,
,且
外接圆的半径为
,
为坐标原点.
(1)求椭圆
的标准方程;
(2)设
为椭圆
上一点,直线
的平行线
与椭圆
相交于
,
两点,直线
,
分别与
轴交于
,
两点,求线段
的中点的纵坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c292f8eb862c09c7ff2d92becacc5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4056761b8f826eeb6ad8c9a151d3c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba1840a13a3025913792f6c9cce21b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
解题方法
7 . 已知椭圆
的左、右焦点分别为
,离心率
,点
在E上.
(1)求E的方程;
(2)过点
作互相垂直且与x轴均不重合的两条直线分别交E于点A,B和C,D,若M,N分别是弦AB,CD的中点,证明:直线MN过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc2210a7e09298897f6585ad08a70d3.png)
(1)求E的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
您最近一年使用:0次
名校
解题方法
8 . 已知椭圆C:
与椭圆
的离心率相同,
为椭圆C上一点.
(1)求椭圆C的方程.
(2)若过点
的直线l与椭圆C相交于A,B两点,试问以AB为直径的圆是否经过定点
?若存在,求出
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9545456fff81a9f9c108f0451dba52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd54a1a3b5f750da1e14552b6066a7c.png)
(1)求椭圆C的方程.
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014608ef148beda3ad9db3ab2efbb2a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2022-12-17更新
|
1728次组卷
|
13卷引用:甘肃省靖远县第一中学等2校2023届高三上学期期末文科数学试题
甘肃省靖远县第一中学等2校2023届高三上学期期末文科数学试题山东省2022-2023学年高二上学期12月质量检测联合调考数学试题北京市中国人民大学附属中学2022-2023学年高二上学期数学期末复习试题(3)山东省济宁市邹城市2022-2023学年高二上学期期末数学试题四川省部分学校2022-2023学年高三上学期12月大联考理科数学试题四川省部分学校2022-2023学年高三上学期12月大联考文科数学试题河北省唐山市部分学校2023届高三上学期12月月考数学试题贵州省毕节市部分学校2023届高三上学期12月联合考试数学(理)试题贵州省毕节市部分学校2023届高三上学期12月联合考试数学(文)试题广东省2022-2023学年高二上学期12月质量检测联考数学试题内蒙古赤峰实验中学、桥北四中2022-2023学年高三下学期大联考数学试题(文科)青海省西宁市大通回族土族自治县2023届高三一模数学(文)试题(已下线)专题15解析几何(解答题)
名校
解题方法
9 . 已知椭圆C:
经过点
,且离心率为
.
(1)求椭圆C的方程;
(2)椭圆C上的两个动点M,N(M,N与点A不重合)直线AM,AN的斜率之和为4,作
于H.问:是否存在定点P,使得
为定值.若存在,求出定点P的坐标及
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求椭圆C的方程;
(2)椭圆C上的两个动点M,N(M,N与点A不重合)直线AM,AN的斜率之和为4,作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41e9c029e8c099fecbf785a18559196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa9e6b473819e4e88341e2d98004de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa9e6b473819e4e88341e2d98004de48.png)
您最近一年使用:0次
2022-11-10更新
|
876次组卷
|
5卷引用:甘肃省酒泉市瓜州县第一中学2024届高三上学期期末数学试题
名校
解题方法
10 . 已知椭圆C:
的离心率为
,点
为椭圆C上一点.
(1)求椭圆C的方程;
(2)若M,N是椭圆C上的两个动点,且
的角平分线总是垂直于y轴,求证:直线MN的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
(1)求椭圆C的方程;
(2)若M,N是椭圆C上的两个动点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45a8a837c11c07073da3ff751d70278.png)
您最近一年使用:0次
2022-03-28更新
|
342次组卷
|
2卷引用:甘肃省民勤县第一中学2021-2022学年高二上学期期末考试数学(理)试题