名校
解题方法
1 . 已知椭圆
:
的左焦点为
,长轴长为
,过右焦点
的直线
交椭圆
于
,
两点
(1)求椭圆
的方程;
(2)设线段
的中点为
,求点
到直线
的距离的取值范围.
![](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/813f9a2814013e2407b5b1c216159359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
您最近一年使用:0次
名校
解题方法
2 . 已知椭圆
的左,右顶点分别为
,左焦点为
,
.
(1)求
的方程;
(2)设直线
与
交于不同于
的
两点,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/816c95fc2267da08690fd80263256b46.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12777a96242feadf7964af7823b7450c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975d6f7561fc2bce5f4c94a33b3c0ccf.png)
您最近一年使用:0次
2023-01-12更新
|
409次组卷
|
2卷引用:陕西省西安市第三十八中学2022-2023学年高三上学期一模数学试题(文科)
名校
解题方法
3 . 已知如图,椭圆
:
,斜率为
的直线
与椭圆
交于
,
两点,与
轴,
轴分别交于
,
两点,若
,则椭圆
的离心率
为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/8b3c8a78-b706-4ccd-a8bf-d763de46baa8.png?resizew=188)
![](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/f89eef3148f2d4d09379767b4af69132.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/1fd5215b49a80c18313fcfd9577886b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/8b3c8a78-b706-4ccd-a8bf-d763de46baa8.png?resizew=188)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
:
的离心率为
,椭圆
的左、右焦点分别为
,
,点
,且
的面积为
.
(1)求椭圆
的标准方程;
(2)过点
的直线
与椭圆
相交于
,
两点,直线
,
的斜率分别为
,
,求
的取值范围.
![](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/c5db41a1f31d6baee7c69990811edb9f.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/2719ce8a1c0aaa60da102db5712d63e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](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/6b881044b5c73db6fcce110525741b02.png)
您最近一年使用:0次
2022-05-31更新
|
497次组卷
|
2卷引用:陕西省西安交通大学附属中学2022届高三下学期第七次模拟考试文科数学试题
5 . 已知椭圆
的上顶点为A,左右焦点分别为
,
,线段
,
的中点分别为
,
,且
是面积为
的正三角形.
(1)求椭圆C方程;
(2)设圆心为原点,半径为
的圆是椭圆C的“基圆”,点P是椭圆C的“基圆”上的一个动点,过点P作直线
,
与椭圆C都只有一个交点.试判断
,
是否垂直?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc48b2f1fe89050e80db7369248c789.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/1f95a62596525307343da7ff4b86cde8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d107e77106ff1a9cb76b504bbc99bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/106aaf32157016d3750f92a951b56d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆C方程;
(2)设圆心为原点,半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
您最近一年使用:0次
名校
6 . 已知椭圆
的一个焦点为
,0),离心率为
.
(1)求椭圆C的标准方程;
(2)若动点P
,
)为椭圆外一点,且点P到椭圆C的两条切线相互垂直,求点P的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c7425ddca80288d614da3bec8d5463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆C的标准方程;
(2)若动点P
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b589732202941f828016f982c92996b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
您最近一年使用:0次
2022-04-14更新
|
766次组卷
|
5卷引用:陕西省渭南市2022届高三下学期二模文科数学试题
陕西省渭南市2022届高三下学期二模文科数学试题(已下线)回归教材重难点04 圆锥曲线-【查漏补缺】2022年高考数学(文)三轮冲刺过关(已下线)专题38 圆锥曲线中的圆问题-1云南省红河哈尼族彝族自治州弥勒市第一中学2021-2022学年高二下学期第四次月考数学试题云南省昭通市市直中学2021-2022学年高二下学期期中考试数学试题
解题方法
7 . 已知椭圆
的右焦点
,且满足
.
(1)求椭圆E的标准方程;
(2)若E上存在M,N两点关于直线
对称,且满足
(O为坐标原点),求l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d241842f57772e0da3898fafa15e63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7e55d1eef2b0b94589d1dd9e7b1b61.png)
(1)求椭圆E的标准方程;
(2)若E上存在M,N两点关于直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f19f6cf445e095c0696b318414ee66a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2abe13e2d4176f55f71677bbbb6eb4.png)
您最近一年使用:0次
8 . 已知椭圆
,若下列四点_________中恰有三点在椭圆C上.
①
;②
.
(1)从①②中任选一个条件补充在上面的问题中,并求出椭圆C的标准方程;
(2)在(1)的条件下,设直线l不经过点
且与椭圆C相交于A,B两点,直线
与直线
的斜率之和为1,过坐标原点O作
,垂足为D(若直线l过原点O,则垂足D视作与原点O重合),证明:存在定点Q,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10137ed8944f28b232b2eefb3310f606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800405f52e3c99775128823093812cc9.png)
(1)从①②中任选一个条件补充在上面的问题中,并求出椭圆C的标准方程;
(2)在(1)的条件下,设直线l不经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.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/6cee097d4fe948c3d4f1b5c28b24adf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5e0909915a39968fee2b2119c20b0c.png)
您最近一年使用:0次
2022-03-30更新
|
1411次组卷
|
3卷引用:陕西省宝鸡中学2022届高三下学期高考关门测试理科数学试题
9 . 已知椭圆
的焦距为2c,左、右焦点分别是
,
,其离心率为
,圆
与圆
相交,两圆的交点在椭圆E上.
(1)求椭圆E的方程.
(2)已知A,B,C为椭圆E上三个不同的点,O为坐标原点,且O为△ABC的重心.证明:△ABC的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.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/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df20ba58b96bb43cfee5c968c3600b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0ae9d467de07587346dac12bcec3b4.png)
(1)求椭圆E的方程.
(2)已知A,B,C为椭圆E上三个不同的点,O为坐标原点,且O为△ABC的重心.证明:△ABC的面积为定值.
您最近一年使用:0次
2022-03-26更新
|
1023次组卷
|
6卷引用:陕西省咸阳市兴平市南郊高级中学2022届高三下学期三模理科数学试题
名校
解题方法
10 . 已知椭圆C:
(
,
)的长轴为双曲线
的实轴,且椭圆C过点P(2,1).
(1)求椭圆C的标准方程;
(2)点A,B是椭圆C上异于点P的两个不同的点,直线PA与PB的斜率均存在,分别记为
,
,且
,当坐标原点O到直线AB的距离最大时,求直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28675c5bcb91f9084684c58095f37ba1.png)
(1)求椭圆C的标准方程;
(2)点A,B是椭圆C上异于点P的两个不同的点,直线PA与PB的斜率均存在,分别记为
![](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/151e09f3a383d7811c619eef3a6398cf.png)
您最近一年使用:0次
2022-03-20更新
|
851次组卷
|
5卷引用:陕西省西安市西北工业大学附属中学2022-2023学年高三上学期第一次适应性训练理科数学试题