2024·全国·模拟预测
名校
解题方法
1 . 已知椭圆
的中心在坐标原点,焦点
在
轴上,点
在
上,长轴长与短轴长之比为
.
(1)求椭圆
的方程.
(2)设
为
的下顶点,过点
且斜率为
的直线与
相交于
两点,且点
在线段
上.若点
在线段
上,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c29ed33ff617aba86b0674543c5d472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da99c7af03730df7a964485b7394c33f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557437a8641a61bf64c1e40f2bbf72a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5600cfbd6016c3470a765d2aedd0aee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75785609aaec8ad40f574e352075bc9.png)
您最近一年使用:0次
解题方法
2 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
的焦距为
,点
在
上.
(1)求
的方程;
(2)点
是
的左顶点,直线
交
于
两点,
分别交直线
于点
,线段
的中点为
,直线
与
轴相交于
点,直线
的斜率为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e454c7161999e2a67138869f59d319b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](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/10b60747933214d7171657b680196577.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/8d42cb68c5c877a455ba7ac0a6b6a651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e08d5c04f0431fb57b33a01717b599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47dfd1be4b77d75ea6194ca3a987cc26.png)
您最近一年使用:0次
名校
解题方法
3 . 在平面直角坐标系xOy中,椭圆
的左焦点为点F,离心率为
,过点F且与x轴垂直的直线被椭圆截得的线段长为3.
(1)求椭圆C的方程;
(2)设不过原点O且斜率为
的直线l与椭圆C交于不同的两点P,Q,线段PQ的中点为T,直线OT与椭圆C交于两点M,N,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆C的方程;
(2)设不过原点O且斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20553e0b4f149dd34c3623676149d43.png)
您最近一年使用:0次
2024-03-25更新
|
928次组卷
|
2卷引用:天津和平区2024届高三一模数学试题
名校
解题方法
4 . 在平面直角坐标系
中,动圆
与圆
内切,且与圆
外切,记动圆
的圆心的轨迹为
.
(1)求轨迹
的方程;
(2)设
为坐标原点,过点
且与坐标轴不垂直的直线与轨迹
交于
两点.线段
上是否存在点
,使得
?若存在,求出
的取值范围;若不存在,说明理由;
(3)过点
且不垂直于
轴的直线与轨迹
交
两点,点
关于
轴的对称点为
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb1a1564d409a8d5908521e3432674f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43bb4c6bab49ddf60492153410604ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4c87b3f7044f650e3b6559df0493a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883f23ab75b490d6e9e03b8ff8b269c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f6aff6bc7b06b8656cf16970e30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61372caa7455964777bb20c15b8e4a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
2024-01-22更新
|
245次组卷
|
2卷引用:山东省东营市2023-2024学年高二上学期1月期末质量监测数学试题
解题方法
5 . 在平面直角坐标系
中,动点
在双曲线
的一条渐近线上,已知
的焦距为4,且
为
的一个焦点,当
最小时,
的面积为
.
(1)求
的方程;
(2)已知点
,直线
与
交于
两点.当
时,
上存在点
使得
,其中
依次为直线
的斜率,证明:
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844a1c77cdc51fb57f2fc55d791ea64f.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/4ac654a052f98d1ccb7fede1f122cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c71c49dc9a9de1a0221769e4eb8616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f96948c49e1a46bd6e52fe47984001c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da73428c941022232136bdd7d0feeba.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/0ad82bfa7f41dd90aa23597cc935105f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7298e9172c5139222535dd653549b9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579e2abe4a57206cfc87fa94fdda6b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
6 . 设点
是椭圆
上任意一点,过点
作椭圆的切线,与椭圆
交于
两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ace6602b-ed9b-4579-a1ec-98d61a6294b3.png?resizew=155)
(1)求证:
;
(2)
的面积是否为定值?若是,求出这个定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e91e565e14d96a20169db44fcde58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ace6602b-ed9b-4579-a1ec-98d61a6294b3.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b0bec6e780130fbed900fdb153555d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2024-02-05更新
|
1467次组卷
|
6卷引用:陕西省西安铁一中学2023-2024学年高二上学期期末考试数学试题
名校
解题方法
7 . 已知椭圆C:
(
)的离心率为
,且点
在椭圆上.
(1)求椭圆C的方程;
(2)若点
,点
在椭圆C上,
轴,垂足为M,直线
交
轴于点N,线段
的中点为坐标原点,试判断直线
与椭圆C的位置关系,并给出证明.
![](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/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
(1)求椭圆C的方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e68223fc39b88b8132d81b019e7f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d1668b8e80d00f85e5836f6ae9dd36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e15d7734d2ef9eb7baa6654149085d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3d566704b44ea4ef1f99c37bd46902.png)
您最近一年使用:0次
2023-12-22更新
|
327次组卷
|
5卷引用:山东省枣庄市薛城实验中学等校2023-2024学年高二上学期12月大联考数学试题
山东省枣庄市薛城实验中学等校2023-2024学年高二上学期12月大联考数学试题河南省周口市西华县第一高级中学等校2023-2024学年高二上学期一月联考数学试题(已下线)第3章:圆锥曲线与方程章末重点题型复习-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)辽宁省2023-2024学年高二下学期期初教学质量检测数学试题山东省临沂市多校2023-2024学年高二上学期12月大联考数学试题
名校
解题方法
8 . 已知椭圆
,长轴长为4, 离心率是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fec9473523620d5d643f9ef87bd46a.png)
(1)求椭圆 C的标准方程;
(2)斜率为
且不过原点的直线
交椭圆C于 A,B两点,线段AB的中点为E,射线OE交椭圆C于点 G,交直线
于点D. 若
证明:直线
经过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fec9473523620d5d643f9ef87bd46a.png)
(1)求椭圆 C的标准方程;
(2)斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893d4e8d70ea2c716ac7b6c1777a77f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8e6dc3b5cea788db724d55f5d31915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-12-22更新
|
1026次组卷
|
5卷引用:北京市东城区景山学校2024届高三上学期12月月考数学试题
北京市东城区景山学校2024届高三上学期12月月考数学试题江苏省盐城市射阳中学2023-2024学年高二上学期第二阶段测试数学试题(已下线)专题03 圆锥曲线题型全归纳(九大考点)-【寒假自学课】2024年高二数学寒假提升学与练(人教A版2019)(已下线)重难点7-2 圆锥曲线综合应用(7题型+满分技巧+限时检测)新疆乌鲁木齐市六校联考2023-2024学年高二上学期期末考试数学试题
9 . 已知椭圆
的左、右顶点分别为A,B,O为坐标原点,点P在C上(异于A,B两点),直线
,
的斜率之积为
,点
在C上.
(1)求C的方程;
(2)过椭圆C的右焦点F的直线
与C交于D,E两点,过线段
的中点G作直线
的垂线,垂足为N,记
的面积为S,直线
,
的斜率分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e67baac84cf5c95d06d50c36cab7c68.png)
(1)求C的方程;
(2)过椭圆C的右焦点F的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e00bf73d03dded1cf5f83cc5339361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.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/ca640540d5152619c1d7eac53a2bdfbd.png)
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解题方法
10 . 椭圆C的方程为
,过椭圆左焦点
的直线与椭圆相交于点P、Q,椭圆的右焦点为
,己知
的周长为8,且椭圆过点
.
(1)求椭圆C中
的值;
(2)过椭圆C的右焦点
作直线l交椭圆C于A,B两点,交y轴于M点,若
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/4fea5f7430235e65d2c2e6b2ecc46712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2412f32502da25289dc11495947ee8e4.png)
(1)求椭圆C中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)过椭圆C的右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b2dacadb6a8b8fe5629931f1455e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
您最近一年使用:0次