名校
解题方法
1 . 已知椭圆
的离心率为
为椭圆
上一点.
(1)求椭圆
的标准方程.
(2)若过点
且斜率为
的直线
与椭圆
相交于
两点,记直线
的斜率分别为
,试问
是否是定值?若是,求出此定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac637017602374d131a7ea838dfeb2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c441c7e1d4bc397894cc8a6a169e0d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaebaf8ceed245eba896f36d8ff14b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b592e1dffca04852b498fba5778fd034.png)
您最近一年使用:0次
2022-05-26更新
|
917次组卷
|
5卷引用:河南省名校联盟2022届高三5月大联考文科数学试题
河南省名校联盟2022届高三5月大联考文科数学试题河南省名校联盟2022届高三5月大联考理科数学试题(已下线)10.6 三定问题及最值(精讲)广西南宁市第三中学2022-2023学年高二上学期期中考试数学试题(已下线)第26讲 圆锥曲线中定值问题(2)
名校
解题方法
2 . 设
、
分别为椭圆
的左、右顶点,设
是椭圆下顶点,直线
与
斜率之积为
.
(1)求椭圆
的标准方程;
(2)若一动圆的圆心
在椭圆上运动,半径为
.过原点
作动圆
的两条切线,分别交椭圆于
、
两点,试证明
为定值.
![](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/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242dc4cf2720b503e26ec8017d31444f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若一动圆的圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a9535f46dcbf08b03cd8b0539663e8.png)
您最近一年使用:0次
2022-05-21更新
|
3396次组卷
|
6卷引用:河南省郑州市2022届高三第三次质量预测理科数学试题
河南省郑州市2022届高三第三次质量预测理科数学试题陕西省西安交通大学附属中学2022届高三下学期全真模拟(二)理科数学试题安徽省合肥市双凤高级中学2022届高三三模文科数学试题(已下线)专题11 圆锥曲线第三定义与点差法 微点1 圆锥曲线第三定义的应用(已下线)专题14 圆锥曲线切线方程 微点3 圆锥曲线切线方程综合训练四川省遂宁市射洪中学校2023届高三下学期开学考试理科数学试题
解题方法
3 . 已知椭圆
的右焦点为
,且点
到坐标原点的距离为
.
(1)求C的方程.
(2)设直线
与C相切于点P,且
与直线
相交于点Q.
①若Q的纵坐标为1,直线FQ与C相交于A,B两点,求
.
②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/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求C的方程.
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6a9687221466a417cc70aa691a0487.png)
①若Q的纵坐标为1,直线FQ与C相交于A,B两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
②判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c32805e421aec6bce3624baa0c954f1.png)
您最近一年使用:0次
2022-05-18更新
|
582次组卷
|
3卷引用:河南省2022届高三下学期仿真模拟考试文科数学试题
名校
解题方法
4 . 已知椭圆
的上下顶点分别为
,
,离心率为
.
![](https://img.xkw.com/dksih/QBM/2022/5/12/2977926716080128/2978535997243392/STEM/52c06ee4e36546d08d79c3e7740dc6a4.png?resizew=200)
(1)求椭圆的标准方程;
(2)过点
且斜率为
的直线
与椭圆交于M,N两点,求证:直线
与直线
的交点T的纵坐标为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37434c0bc2a8f4b8e5f16f16dc3d9b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d503ab387c5cac181bb983989ecd499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://img.xkw.com/dksih/QBM/2022/5/12/2977926716080128/2978535997243392/STEM/52c06ee4e36546d08d79c3e7740dc6a4.png?resizew=200)
(1)求椭圆的标准方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e884ca9429486026caa5e2310b0e4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201d7685f19582f5d54f9205e8598d5a.png)
您最近一年使用:0次
2022-05-13更新
|
372次组卷
|
2卷引用:河南省多校联盟2022届高考终极押题(A卷)数学(文)试题
名校
5 . 已知点D为圆O:
上一动点,过点D分别作
轴、
轴的垂线,垂足分别为A、B,连接BA并延长至点P,使得
,点P的轨迹记为曲线C .
(1)求曲线C的方程;
(2)设直线l与曲线C交于不同于右顶点Q的M,N两点,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.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/2b9e63f8aa053688faaa75be638e7c3e.png)
(1)求曲线C的方程;
(2)设直线l与曲线C交于不同于右顶点Q的M,N两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40de95d0e65c07fe954e4643a3bb6ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f07baa8b45a039974d841a2ab024d4.png)
您最近一年使用:0次
2022-05-12更新
|
504次组卷
|
2卷引用:河南省南阳市第一中学校2022届高三下学期第三次模拟考试文科数学试题
名校
解题方法
6 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
经过两点
和
.
(1)求椭圆
的方程;
(2)设直线
经过椭圆
的右焦点
,且与椭圆
交于不同的两点
、
,在
轴上是否存在点
,使得直线
与直线
的斜率的和为定值?若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434249d6640b0c1a712d215cf8b83d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd5f27c5f8a8cda3403c73108dfd30c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1721aa6b62fc4c68cb7161f2658117.png)
(1)求椭圆
![](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/a0ed1ec316bc54c37c4286c208f55667.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2022-05-12更新
|
454次组卷
|
2卷引用:河南省百所名校2022届普通高校招生全国统一考试猜题压轴卷理科数学试题
名校
7 . 已知椭圆
的离心率为
,长轴右端点到左焦点的距离为
.
(1)求椭圆
的方程;
(2)点
是圆
上的一点,过
作圆
的切线
,且切线
与椭圆
交于
、
两点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab46ea0cba2d06283fae3d864a2329e0.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc64ba34f941b2ac154f8d7bc99f915d.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/0f85fca60a11e1af2bf50138d0e3fe62.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/3825ccc273ef9a672a606432d165b866.png)
您最近一年使用:0次
名校
解题方法
8 . 已知椭圆
为其左焦点,
在椭圆C上.
(1)求椭圆C的方程.
(2)若A,B是椭圆C上不同的两点,O为坐标原点,若
,是否存在某定圆始终与直线
相切?若存在,求出该定圆的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154ac58b9ab50db5ced5291ca81d03ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
(1)求椭圆C的方程.
(2)若A,B是椭圆C上不同的两点,O为坐标原点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1695034a4c212e5568fe41625fd2a417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
9 . 已知椭圆
,
为其左焦点,
在椭圆
上.
(1)求椭圆C的方程.
(2)若A,B是椭圆C上不同的两点,O为坐标原点,且
,问△OAB的面积是否存在最大值?若存在,求出这个最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆C的方程.
(2)若A,B是椭圆C上不同的两点,O为坐标原点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1695034a4c212e5568fe41625fd2a417.png)
您最近一年使用:0次
2022-05-08更新
|
1392次组卷
|
11卷引用:河南省汝州市2022届高三5月模拟考试理科数学试题
10 . 已知椭圆
与抛物线
交于y轴上的同一点M,过坐标原点O的直线l与
相交于点A,B,直线MA,MB分别与
相交于点D,E.
(1)①求椭圆
与抛物线
的方程;
②证明:MD,ME的斜率之积为定值.
(2)记△MAB、△MDE的面积分别为
、
,求
的最小值,并求取最小值时直线MA的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c581bb052acef875f5ec8fd71c8f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bffa568526e99c96ab165fd4e157c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)①求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
②证明:MD,ME的斜率之积为定值.
(2)记△MAB、△MDE的面积分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7051f87f98ce95dd93e9b3eb288cd322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c82d23048474422a160840aa4d8aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1d67952280135370cc08884dc0936a.png)
您最近一年使用:0次