名校
解题方法
1 . 已知椭圆的方程为
,
为椭圆短轴顶点,
为椭圆
的右顶点
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00857b232a86db6a924b34320f928717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22f3e397e5d4b120f92a40657eaf7aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a67260be97cca75002f4814d1b0418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6d6a0ee7672e93d79d51b938d9299e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10416030bbf5df1fb9cb66e0220bbd95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05afb62c4e3a66a50cd0252762324bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
您最近一年使用:0次
23-24高二·全国·假期作业
名校
解题方法
2 . 已知点的坐标分别是
,
,直线
相交于点M,且它们的斜率之积为
.
(1)求点M轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269a51e0f77f63bae2df3dc8b1d4f455.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e00bf73d03dded1cf5f83cc5339361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f239a35de1828b14a58be5bd5af9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
2024-01-01更新
|
731次组卷
|
3卷引用:专题10 圆锥曲线综合大题10种题型归类-【寒假分层作业】2024年高二数学寒假培优练(人教A版2019选择性必修第一册)
(已下线)专题10 圆锥曲线综合大题10种题型归类-【寒假分层作业】2024年高二数学寒假培优练(人教A版2019选择性必修第一册)(已下线)专题11椭圆(3个知识点7个拓展2个突破7种题型2个易错点)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(人教A版2019选修第一册)江西省赣州市南康中学2024届高三上学期"七省联考"考前数学猜题卷(十)
名校
解题方法
3 . 已知椭圆:
的离心率是
,点
是椭圆的上顶点,点
是椭圆上不与椭圆顶点重合的任意一点.
(1)求椭圆
的方程;
(2)设圆
.若直线
与圆
相切,且点
在
轴右方,求点
的坐标;
(3)若点
是椭圆
上不与椭圆顶点重合且异于点
的任意一点,点
关于
轴的对称点是点
,直线
、
分别交
轴与点
、点
,探究
是否为定值,若为定值,求出该定值,若不为定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca7e0ff6a7539423620b5ecfe0ea1ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d4d459703d0d9793b807248b874bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5850ed6ad7d8e9652625bd03766c61df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851aa470283a8993975229cdad3021e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb74ca8fc86ddef279e33f31c1fedda.png)
您最近一年使用:0次
名校
解题方法
4 . 已知抛物线
的焦点为
,点
满足
.
(1)求
的值及
的方程;
(2)若过点F的直线l交C于M,N两点,求
的最小值及此时直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4adf350d93f854ac0cb48a5c7435e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba230d3c7486e405c988524523e8f97.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点F的直线l交C于M,N两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e6f0e94393fc6bbd9b4b83ede534ac.png)
您最近一年使用:0次
5 . 以坐标原点为对称中心,坐标轴为对称轴的椭圆过点
.
(1)求椭圆的方程.
(2)设
是椭圆上一点(异于
),直线
与
轴分别交于
两点.证明在
轴上存在两点
,使得
是定值,并求此定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3b351f66cf98455d42660520b5ff0c.png)
(1)求椭圆的方程.
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e7344dca1e40bf072371ddd5640111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf9f7adfb1276af4d84ce859e6b4247.png)
您最近一年使用:0次
2023-10-19更新
|
992次组卷
|
5卷引用:云南省昆明市第三中学2023-2024学年高二上学期1月期末考试数学试卷
6 . 已知椭圆E:
,椭圆上有四个动点A,B,C,D,
,AD与BC相交于P点.如图所示.
(2)若点P的坐标为
,求直线AB的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d12ebd10f6c0bcf98be52c32b107f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
(2)若点P的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba31c1dd27defc2621e4fb4d7006f7f1.png)
您最近一年使用:0次
2023-06-03更新
|
837次组卷
|
5卷引用:江苏省淮安市淮阴中学2023-2024学年高二上学期10月阶段练习数学试题
名校
解题方法
7 . 如图,四边形
中,
,三角形
为正三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/77b6ceaa-fc31-4745-b896-919cfa197570.png?resizew=146)
(1)当
时,设
,求
的值;
(2)设
,则当
为多少时.
①四边形
的面积
最大,最大值是多少?
②线段
的长最大,最大值是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea16ceca816f7d3d50650af141baf42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026f31fbff5d5759500caed28f19459f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/77b6ceaa-fc31-4745-b896-919cfa197570.png?resizew=146)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc790cfaa59a808c25a7edb95dc29fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450743dbe1916012643039cd87a72263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d708cb763716467219215cdc0782c0a6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2038b7b362e7af5b747a3ab8857f2e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
①四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea16ceca816f7d3d50650af141baf42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
②线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
您最近一年使用:0次
2023-04-21更新
|
921次组卷
|
3卷引用:江苏省镇江第一中学2022-2023学年高二下学期期中校际联考数学试题
名校
8 . 如图所示的矩形
中,
分别为线段
上的动点.
为靠近
的三等分点,
为
的中点,且
,求
的值;
(2)若
是边长为1的正三角形.
(i)令
、
、
的面积分别为
,
,
,证明:
;
(ii)求矩形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c562ffebf701e6d812eed6fc898fb42b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
(i)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13668f033d00acfc366f7e47949c4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d85bcd207e761df740d87a6acb81bf7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485fd8aa254b523bef30560500ccaf41.png)
(ii)求矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-04-19更新
|
1040次组卷
|
4卷引用:广东省惠州大亚湾经济技术开发区第一中学2023-2024学年高二上学期第一次月考数学试题
广东省惠州大亚湾经济技术开发区第一中学2023-2024学年高二上学期第一次月考数学试题江苏省南京市协同体七校2022-2023学年高一下学期期中联考数学试题(已下线)模块四 高一下期中重组篇(江苏)(已下线)专题4 考前优质试题精选练(4)(北师大版高一期中)
名校
解题方法
9 . 已知
为坐标原点,对于函数
,称向量
为函数
的伴随向量,同时称函数
为向量
的伴随函数.
(1)设函数
,试求
的伴随向量
;
(2)记向量
的伴随函数为
,求当
且
时,
的值;
(3)当向量
时,伴随函数为
,函数
,求
在区间
上最大值与最小值之差的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66655b7a6825b124ce596197bf2aa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e55ab02325419a2e1e99077f2f35fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(2)记向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffe91c3b3290e5eb048b0028b0a5686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a23ec821b5896710d79bfe703cec01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3fa686db08faac289451eb2d93e764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8c56d09485b718a85ed23f637e2d77.png)
(3)当向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5403216cc93a9413ca330fc13b0df29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c691f19308f093ef6c3a77a519fb79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07286db2a5af137e599d59ea52b08a33.png)
您最近一年使用:0次
2023-04-14更新
|
1075次组卷
|
10卷引用:江苏省南通市2022-2023学年高二下学期期末模拟数学试题
江苏省南通市2022-2023学年高二下学期期末模拟数学试题广东省广州市第六中学2023-2024学年高二上学期期中数学试题湖北省孝感市2022-2023学年高一下学期期中联考数学试题福建省泉州市培元中学2022-2023学年高一下学期5月月考数学试题(已下线)模块二 专题2 三角函数恒等变换 单元检测篇 A基础卷 (苏教版)四川省眉山市青神县青神中学校2022-2023学年高一下学期期中数学试题江西省抚州市东乡区实验中学2022-2023学年高一下学期期中数学试题江苏省连云港高级中学2022-2023学年高一下学期期中数学试题江苏省苏州昆山柏庐高级中学2023-2024学年高一下学期3月月考数学试题广东省佛山市南海区罗村高级中学2023-2024学年高一下学期阶段测试(一)数学试题
名校
解题方法
10 . 已知点
为中心在坐标原点的椭圆C的焦点,且椭圆过点
.
(1)求椭圆C的标准方程;
(2)过点F作直线
与椭圆C交于A,B两点,设
,若
,点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e641014eb998f16c14ee0ec59f9d54f0.png)
(1)求椭圆C的标准方程;
(2)过点F作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ec81508b65d234b67019c332fab0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d42bc65aa8383f8ee41a1115f01d06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1400bea62e9e0bf6c924b796045b3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3d743bf924a625f564e62b9f5d8655.png)
您最近一年使用:0次