解题方法
1 . 已知曲线
由半圆
和半椭圆
组成,点
在半椭圆上,
,
.
的值;
(2)
在曲线
上,若
(
是原点).
(ⅰ)求
的取值范围;
(ⅱ)如图,点
在半圆上时,将
轴左侧半圆沿
轴折起,使点
到
,使点
到
,且满足
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264440f5af29bbdd38635ab6e5d31851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1dda09e3eb7a46e07422742d46f4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57173ef4cd72eb270686875dfd623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb898663f98b8400a897913b4d3102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67761f75cee6201ec2b2dbf40db77c0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb40dae2b0f4048d3fabff25e6cbe443.png)
(ⅱ)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b1ba4307cfde9b424d468bfcdf6c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81154c32dcbe56cb5c392b9388ca4475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22285c8766c10ccaaddd6ad47d20f9f1.png)
您最近一年使用:0次
2 . 如图所示,点P在椭圆
上移动,点Q在以点
为圆心,半径为
的圆上移动,当点P位于点
,点Q位于点
时,P、Q两点距离最近,记最近距离为d,求d及
、
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c9dcfd9f4c5298035870cb88a34169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c9298da3cd8b9db58692e0173f3fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762bfc20a2da28b3c59225851ea40036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5f711090b19d6735a0b86cad4af321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762bfc20a2da28b3c59225851ea40036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5f711090b19d6735a0b86cad4af321.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/6a611a89-f350-4193-b9b8-8a4315e87ebc.png?resizew=159)
您最近一年使用:0次
名校
解题方法
3 . 已知曲线
:
.
为双曲线,且渐近线方程为
,求曲线
的离心率;
(2)若曲线
为椭圆,且
在曲线
上.过原点且斜率存在的直线
和直线
(
与
不重合)与椭圆
分别交于
,
两点和
,
两点,且点
满足到直线
和
的距离都等于
,求直线
和
的斜率之积;
(3)若
,过点
的直线与直线
交于点
,与椭圆交于
,点
关于原点的对称点为
,直线
交直线
交于点
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166364a7131344022a246283018d32f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b75308335340230171130238f4dc6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843384d54dfc753f24f7071fd19b97c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5745b2dc86ddc6845c8594eaaab146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d0aa9412dd7caf42cc71520e282328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d0aa9412dd7caf42cc71520e282328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb40dae2b0f4048d3fabff25e6cbe443.png)
您最近一年使用:0次
4 . 已知
的两个顶点
,
,点G为
的重心,边
上的两条中线的长度之和为6,记点G的轨迹为曲线E.
(1)求曲线E的方程;
(2)若点P是曲线E上的任意一点,
,
,
,
,直线PC,PD与x轴分别交于点M,N.
①求
的最大值;
②判断
是否为定值.若为定值,求出该定值;若不为定值,求出它的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8dfd0ebf16476994cf04dd0f7fafca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13683e2ecf2164a0adbfdb9923d210a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8dfd0ebf16476994cf04dd0f7fafca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6bf421591c540d317587bdac885e9c.png)
(1)求曲线E的方程;
(2)若点P是曲线E上的任意一点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dbc9361f0be545e55976a052e95e960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a375e47ac52f067ac1f7b3f73dbc41ee.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
②判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9467e420cfaea81eb1e7245e3f14c503.png)
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5 . 已知
,
,直线l:
,动点P到l的距离为d,满足
,设点P的轨迹为C,过点F作直线
,交C于G,H两点,过点F作与
垂直的直线
,直线l与
交于点K,连接AG,AH,分别交直线l于M,N两点.
(1)求C的方程;
(2)证明:
;
(3)记
,
的面积分别为
,
,四边形AGKH的面积为
,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d743a88d9d8aba9a3887a3638375e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6bbbb53aaeab0ab7a242228cc510fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051be09b4e835cf68f624541a843018d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b99ef417ec17cd7c7caf2b17ee00bc9.png)
![](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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(1)求C的方程;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1deb868aceb01c55bf8d859871a20ff6.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e72388cdb40f730d3a8fed7d61fba14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffa4f0665d2a639b540b950dda3e5c4.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/8a7b29bde8f4bdcc610618087398df91.png)
您最近一年使用:0次