1 . 对于曲线
,下面说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a2a1681af283bc90d6a6abad13c218b.png)
A.若![]() ![]() |
B.若曲线![]() ![]() ![]() |
C.若曲线![]() ![]() ![]() ![]() |
D.若曲线![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
2 . 设
,
是椭圆
(
)的左、右焦点,过
的直线
与
交于
,
两点,若
,
,则
的离心率为( )
![](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/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85d02822aed80dc070e71f496310bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa7d147008033bfc05fe96632c28480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
3 . 已知椭圆
的对称中心为坐标原点,焦点在
轴上,
的离心率为
,且过点
, 等轴双曲线
以
的焦点
、
为顶点,动点
在
的右支上且异于顶点.
与
的方程;
(2)设直线
、
的斜率分别为
、
,直线
与
相交于点
、
,直线
与
相交于点
、
. 是否存在常数
使得
,若存在求出
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a68871af61de95498d346f2eb451aad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a30de57df4e6f60bffe9ac591b24fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8387b687579c4d5152175c9d19e24232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b87502d85db80837ca6f2199ed6c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc01a3c73d759970e5d84f333cce2d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb85b3fa748136b2f6189c55634eb259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87e0c79fdd8e028e234947bd9c4504b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.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/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4091c4e9de55a1ec9872eb3e7bcb5b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68bdb2733ca0f672a599d279ae493ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
您最近一年使用:0次
4 . 已知椭圆
的左、右焦点分别为
,
,离心率为
,点
,且
为等腰直角三角形.
(1)求椭圆
的标准方程;
(2)设点
为
上的一个动点,求
面积的最大值;
(3)若直线
与
交于
两点,且
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20a7cb8494b71121a4d176f923d4318.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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50667ce76318b23b69ac6b8e16dc80d0.png)
(3)若直线
![](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/3c27ca17526003f779a0b68993a26180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
7日内更新
|
308次组卷
|
5卷引用:湖南省岳阳市第一中学等多校2023-2024学年高二下学期5月月考数学试题
(已下线)湖南省岳阳市第一中学等多校2023-2024学年高二下学期5月月考数学试题河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题河南省部分重点高中2023-2024学年高二下学期5月质量检测数学试题山西省临汾市部分学校2023-2024学年高二下学期5月质量检测数学试题(已下线)模型6 非对称结构和齐次化处理问题模型
5 . 已知椭圆
过点
,离心率为
.不过原点的直线
交椭圆
于
两点,记直线
的斜率为
,直线
的斜率为
,且
.
(1)证明:直线
的斜率
为定值;
(2)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.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/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a350d44bf2b7ddfbfe23c754efa9c8d4.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
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名校
解题方法
6 . 已知椭圆
的左、右焦点分别为
为上顶点,离心率 为
,直线
与圆
相切.
(1)求椭圆
的标准方程;
(2)椭圆方程
,平面上有一点
. 定义直线方程
是椭圆
在点
处的极线.
① 若
在椭圆
上,证明: 椭圆
在点
处的极线就是过点
的切线;
② 若过点
分别作椭圆
的两条切线和一条割线,切点为
,割线交椭圆
于
两点,过点
分别作椭圆
的两条切线,且相交于点
. 证明:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d81afe11925b30336768531ede1c278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72dcc2ad9bd83bf683a3c10aebf1c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70993bac22dd8e80a4d151900785a7fb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62645f10a184693406c85b90386b43d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f137ff5fe9fd34a482228e24e9a55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74b54fca09a55c3720426e2dc4dfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f137ff5fe9fd34a482228e24e9a55b.png)
① 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f137ff5fe9fd34a482228e24e9a55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/dad2a36927223bd70f426ba06aea4b45.png)
② 若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eebd2e8567f55a4499c51e3c4eed6c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55c23f1782d16f190469765e02b8c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.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/6f90c72d708d6d7693d4727ae7882317.png)
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名校
解题方法
7 . 已知椭圆
的离心率为
,过
的左焦点且斜率为1的直线与
交于
两点.若
,则
的焦距为__________ .
![](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/c5db41a1f31d6baee7c69990811edb9f.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/58168edb2306922360573f6ba14e90c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2024-06-13更新
|
71次组卷
|
2卷引用:2024届湖南省长沙市第一中学高考最后一卷数学试题
名校
8 . 设椭圆
与双曲线
有相同的焦距,它们的离心率分别为
,
,椭圆
的焦点为
,
,
,
在第一象限的交点为
,若点
在直线
上,且
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8210484dd6815b5bebc7b22f1389cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82b84d8369b8792d0296638dd0fbe43.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f9bdc6d9f09e14b037ea7d3ee1f623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a708c976cfe1b2741cb79d078db8e453.png)
A.2 | B.3 | C.![]() | D.![]() |
您最近一年使用:0次
2024-06-12更新
|
136次组卷
|
2卷引用:湖南省长沙市长郡中学2024届高三下学期二模考试数学试题
名校
解题方法
9 . 已知椭圆
)的左、右顶点分别为A,B,左焦点为F,P为椭圆上一点,直线
与直线
交于点M,
的角平分线与直线
交于点N.若
,
的面积是
面积的
倍,则椭圆C的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d4ab4f05dbd1a4301ed0dc4c73aa75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80406e8beb743b122bd7b021671c780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48783d1e42a271661f3b162501c06032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
10 . 在平面直角坐标系中,已知两定点
,
,动点P到
,
的距离之和为
,若存在一点P满足
的面积为
,写出满足条件的一个动点P的轨迹方程______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.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/bd95e24f73f48167eb193951bd4fa7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acffd1c81e176e4f7dcc32faca34ddc0.png)
您最近一年使用:0次