名校
解题方法
1 . 已知椭圆
的中心为坐标原点,对称轴为
轴,
轴,且过
两点.
(1)求椭圆
的方程;
(2)
为椭圆
的右焦点,直线
交椭圆
于
(不与点
重合)两点,记直线
的斜率分别为
,若
,证明:
的周长为定值,并求出定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/b34fe4f6b7442067e0974d3205d56ea9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73effce2c69e6918c748df4d22320703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595ba5dc88bf92a4d6a32b81ca103f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab71adfe532cd5346fc315ed1264fb52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a9bf6bda9363dbef5f6ff4bf6a5edf.png)
您最近一年使用:0次
2022-09-28更新
|
3206次组卷
|
16卷引用:河南省周口恒大中学2022-2023学年高二上学期期末考试数学试题
河南省周口恒大中学2022-2023学年高二上学期期末考试数学试题河南省南阳市第一中学校2023届高三下学期开学考试理科数学试题河南省南阳市宛城区南阳市第一中学校2023届高三下学期开学考试文科数学试题河南省周口市川汇区周口恒大中学2023-2024学年高二上学期12月月考数学试题河南省信阳市新县高级中学2024届高三下学期模拟考试一数学试题重庆市第八中学校2023届高三上学期高考适应性月考(一)数学试题湖北省武汉市第一中学2022-2023学年高三上学期10月月考数学试题辽宁省葫芦岛市四校2022-2023学年高二上学期期中联考数学试题(已下线)专题32 一类与斜率和、差、商、积问题的探究-1湖南师范大学附属中学2022-2023学年高三上学期月考(三)数学试题湖南省衡阳师范学院祁东附属中学2023届高三下学期2月高考模拟数学试题河北省石家庄市第二中学2022-2023学年高三上学期期中考试数学试题(已下线)广东省2022届高三一模数学试题变式题17-22安徽省安庆市第二中学2022-2023学年高三下学期第七次质量检测数学试题(已下线)专题3.16 圆锥曲线中的定点、定值、定直线问题大题专项训练(30道)-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)专题3.5 直线与椭圆的位置关系-重难点题型精讲-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)
名校
解题方法
2 . 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
解题方法
3 . 已知椭圆
的离心率为
,
、
分别为椭圆的左、右焦点,
为椭圆上在第一象限内的任意一点,且
的周长为
.
(1)求
的方程;
(2)已知点
,若不过点
的直线
与
交于
、
两点,且
,证明:直线
过定点.
![](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/f5076289823db419f94e9c0c8f4aafd9.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb6f3d7540831a9e97d3b184a491.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242dc4cf2720b503e26ec8017d31444f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/3966ea93906bbf9f197992ffa3013a3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-07-13更新
|
1706次组卷
|
5卷引用:河南省安阳市滑县2021-2022学年高二下学期期末数学文科试题
河南省安阳市滑县2021-2022学年高二下学期期末数学文科试题河南省安阳市滑县2021-2022学年高二下学期期末数学理科试题(已下线)专题18 圆锥曲线中的张角问题 微点3 圆锥曲线中的张角问题综合训练(已下线)专题9-5 圆锥曲线大题基础:定点归类(已下线)第25讲 圆锥曲线直线圆过定点问题-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)
解题方法
4 . 已知椭圆
的离心率为
,左、右焦点分别为曲线
与x轴的两个交点.
(1)求C的方程;
(2)点P是圆
上的动点,过点P作C的两条切线,两条切线与圆O分别交于点A,B(异于P),证明:
为定值.
![](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/b610a7ba9eab50424b71499c8d88d272.png)
(1)求C的方程;
(2)点P是圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad88c1b6864919a5fc94e29cb9bf4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
2022-06-20更新
|
400次组卷
|
3卷引用:河南省焦作市2021-2022学年高二下学期期末数学文科试题
解题方法
5 . 已知椭圆
的离心率
,且经过点
.
(1)求C的方程;
(2)直线
交椭圆C于P,Q两点,点P,E关于原点对称,若直线ME与MQ的斜率分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b85acb5a868b0ff2a17b1ca926dd43.png)
(1)求C的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ff33c080c560fccd8d9bf3b08a2886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37ca2bbaa102db55f920aa0bc5ad0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498d92fc9cbc71d623104bae063133dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bffbcbb953bc85c121c31c0b56401e.png)
您最近一年使用:0次
2022-07-03更新
|
353次组卷
|
2卷引用:河南省平顶山市2021-2022学年高二下学期期末数学文科试题
解题方法
6 . 已知椭圆
的离心率是
,直线
被椭圆
截得线段长度为
.
(1)求椭圆
的标准方程;
(2)设点
为椭圆的上顶点,过定点
)且斜率存在的直线
(不经过点
)与椭圆交于
两点,求证:直线
的斜率之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8741897fe31c3c53e1b715dc6bc0f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/85dde9d5e2426cc9da23014b91f03f9e.png)
您最近一年使用:0次
名校
解题方法
7 . 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(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
名校
解题方法
8 . 已知椭圆
:
,四点
,
,
,
中恰有三点在椭圆
上.
(1)求椭圆
的方程;
(2)若点
为
的左焦点,点
为
上位于第一象限的一点,M,N为y轴上的两个动点(点M在
轴上方),满足
,
,线段PN交x轴于点Q.求证:
为定值.
![](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/4dd58baea326536a3eb40b486c4d5905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e5cdcc3cf3ca21f12edaf5397ddbd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ce4ca242277f5a197b70a6431c24bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3835e6398d18d162afebc92cd2ae9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb333b87ab3ecde430010b4dd8b371fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875fef553247cebf93e84175ac409875.png)
您最近一年使用:0次
2022-03-21更新
|
464次组卷
|
3卷引用:河南省部分名校2022届高三下学期3月质量检测理科数学试题
名校
解题方法
9 . 椭圆C:
(
)的左右焦点分别为
,
,上顶点为A,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/7575d0b3-e787-46b9-bda7-5bc220c525d5.png?resizew=222)
(1)求C的方程;
(2)若椭圆E:
(
且
),则称E为C的
倍相似椭圆,如图,已知E是C的3倍相似椭圆,直线l:
与两椭圆C,E交于4点(依次为M,N,P,Q,如图).且
,证明:点T(k,m)在定曲线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2644e9f73e5871db934fdafc431d675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7727c567492eb0a91265983ef8f7b4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/7575d0b3-e787-46b9-bda7-5bc220c525d5.png?resizew=222)
(1)求C的方程;
(2)若椭圆E:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b6494c8078692621054e98b8d0d874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472393b18c7880e73b40e31fbe2d951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e87fec9f747583c5cf3e3f23af85dce.png)
您最近一年使用:0次
2022-12-27更新
|
651次组卷
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3卷引用:河南省部分学校2022-2023学年高三12月大联考文科数学试题
解题方法
10 . 已知椭圆
的离心率
,且过点
.
(1)求
的方程;
(2)已知点
,直线
与
交于
、
两点,若
的平分线垂直于
轴,证明:
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783750d7a4e8dfd0250ad59304c31491.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/bfe82457b26bc0282d97107570204d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-06-20更新
|
615次组卷
|
5卷引用:河南省安阳市2021-2022学年高二下学期阶段性测试(五)文科数学试卷
河南省安阳市2021-2022学年高二下学期阶段性测试(五)文科数学试卷河南省安阳市2021-2022学年高二下学期阶段性测试(五)理科数学试卷(已下线)知识点:直线与圆锥曲线关系 易错点3 恒成立意义不明导致定点问题错误(已下线)突破3.1 椭圆(重难点突破)-【新教材优创】突破满分数学之2022-2023学年高二数学重难点突破+课时训练 (人教A版2019选择性必修第一册)(已下线)第25讲 圆锥曲线直线圆过定点问题-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)