1 . 如图,动 双曲线的一个焦点为
,另一个焦点为
,若该动双曲线的两支分别经过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/14/f53ba40d-ff0c-4c90-9d8c-c994047155f5.png?resizew=157)
(1)求动点
的轨迹方程;
(2)斜率存在且不为零的直线
过点
,交(1)中
点的轨迹于
两点,直线
与
轴交于点
,
是直线
上异于
的一点,且满足
.试探究是否存在确定的
值,使得直线
恒过线段
的中点,若存在,求出
值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206b15b98ea0dc1df707ebf9a639a7b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deefe9a9c7625ba0fe4d24d989ae12ff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/14/f53ba40d-ff0c-4c90-9d8c-c994047155f5.png?resizew=157)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)斜率存在且不为零的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c9dcfd9f4c5298035870cb88a34169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5f1981718bc1419576224cc173d044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1fab515da61355295ef3c95243810e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-05-12更新
|
1669次组卷
|
2卷引用:安徽省黄山市2023届高三三模数学试题
2 . 焦点在
轴上的椭圆
的左顶点为
,
,
,
为椭圆上不同三点,且当
时,直线
和直线
的斜率之积为
.
(1)求
的值;
(2)若
的面积为1,求
和
的值;
(3)在(2)的条件下,设
的中点为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a032dd225bdd793172220c494c2054e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c16dac1e9bf5804c8907cbc59014d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b49ade408d775b9fd5f51832378dc8d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c847f857b8d1788d4ba414b82840ef5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e8fd7b0f5e19e98eebbe844b2e5347.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c2fe11e474108ac0a3d3d538090250.png)
您最近一年使用:0次
2024-03-26更新
|
1062次组卷
|
4卷引用:辽宁省鞍山市第六中学2024届高三下学期第二次质量检测数学试题卷
解题方法
3 . 已知曲线C:
,从曲线C上的任意点
作压缩变换
得到点
.
(1)求点
所在的曲线E的方程;
(2)设过点
的直线
交曲线E于A,B两点,试判断以AB为直径的圆与直线
的位置关系,并写出分析过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204dbf02042c70400b167d2d04fd1a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3682b5a7157ec7cf8b265bf0d1025c.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3682b5a7157ec7cf8b265bf0d1025c.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7422cbdb4ad06d155abb2ccdb25ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
您最近一年使用:0次
4 . 已知椭圆
:
,直线
:
交椭圆于M,N两点,T为椭圆的右顶点,
的内切圆为圆Q.
(1)求椭圆
的焦点坐标;
(2)求圆Q的方程;
(3)设点
,过P作圆Q的两条切线分别交椭圆C于点A,B,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b801e3da6f1b42d1f68cbf88cbfb4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bf66a5f30d94390f59c6a3d1ae6c46.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求圆Q的方程;
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cc4e8043fb27abccf766c5f314dfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
您最近一年使用:0次
名校
解题方法
5 . 已知椭圆
的中心为
,离心率为
.圆
在
的内部,半径为
.
,
分别为
和圆
上的动点,且
,
两点的最小距离为
.
(1)建立适当的坐标系,求
的方程;
(2)
,
是
上不同的两点,且直线
与以
为直径的圆的一个交点在圆
上.求证:以
为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/0b80f580d0f5279d4a8fc07efdd9ca2e.png)
(1)建立适当的坐标系,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-04-03更新
|
1524次组卷
|
4卷引用:福建省2022届高三诊断性检测数学试题
福建省2022届高三诊断性检测数学试题(已下线)临考押题卷06-2022年高考数学临考押题卷(新高考卷)(已下线)必刷卷01-2022年高考数学考前信息必刷卷(新高考地区专用)福建省晋江市季延中学2022-2023学年高二上学期期中考试数学试题
解题方法
6 . 已知直线
交椭圆
于
,
两点,
是直线
上一点,
为坐标原点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2242ca20bd7ab3d41b128e10a4071521.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.椭圆![]() ![]() |
B.![]() |
C.![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-01-15更新
|
587次组卷
|
2卷引用:2023年普通高等学校招生全国统一考试·新高考仿真模拟卷数学(六)
7 . 已知椭圆
的方程为
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/d0b1f36d-b345-4b0d-a430-34a4d6718812.png?resizew=237)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/5746b78d-f94b-488f-abce-a1cad298b5e8.png?resizew=236)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/d4ba530b-f4a7-4281-ac34-ada03587e915.png?resizew=264)
(1)设
是椭圆
上的点,证明:直线
与椭圆
有且只有一个公共点;
(2)过点
作两条与椭圆只有一个公共点的直线,公共点分别记为
、
,点
在直线
上的射影为点
,求点
的坐标;
(3)互相垂直的两条直线
与
相交于点
,且
、
都与椭圆
只有一个公共点,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/d0b1f36d-b345-4b0d-a430-34a4d6718812.png?resizew=237)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/5746b78d-f94b-488f-abce-a1cad298b5e8.png?resizew=236)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712321353637888/2718228101832704/STEM/d4ba530b-f4a7-4281-ac34-ada03587e915.png?resizew=264)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bc97d4acc37ccb7480571754737cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da744f1fe4ccafc57429536ff249ecd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6fcc80c8f221bfd1c575b7c95fbe66b.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)互相垂直的两条直线
![](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/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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
8 . 在平面直角坐标系xOy中,点A在
轴上滑动,点B在
轴上滑动,A、B两点间距离为
.点P满足
,且点P的轨迹为C.
(1)求C的方程;
(2)设M,N是C上的不同两点,直线MN斜率存在且与曲线
相切,若点F为
,那么
的周长是否有最大值.若有,求出这个最大值,若没有,请说明理由.
![](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/d0fe1e989d7fe8a9eb35cb5cf0f9cdaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14379628d6b903f4348eed12b3bc733.png)
(1)求C的方程;
(2)设M,N是C上的不同两点,直线MN斜率存在且与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb374fd349306abf2f784b6a28d93a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33181b27b10690b4913595f8c1f46e.png)
您最近一年使用:0次
9 . 已知椭圆
的焦距为2,离心率为
如图,在矩形ABCD中,
,
,E,F,G,H分别为矩形四条边的中点,过E做直线交x轴的正半轴于R点,交椭圆于M点,连接GM交CF于点T
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/5/6821999f-b323-4574-9616-d69ef6f9c49d.png?resizew=164)
(1)求椭圆的标准方程;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad51c072fc094bae0e45c1d1cc174823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7f6fca0cb9ee43e61cdc8f63ef8d51.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/5/6821999f-b323-4574-9616-d69ef6f9c49d.png?resizew=164)
(1)求椭圆的标准方程;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e0fb1dac3d81b4613a751263402a0c.png)
您最近一年使用:0次
解题方法
10 . 已知动点M的坐标满足方程
,直线
:
,过点
且方向向量为
的直线
与动点M的轨迹交于A,B两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f4fc03beba369a4aa17fb039bb37aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44400e1d547e3c88d31df752f235d624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
A.动点M的轨迹是一条抛物线 |
B.直线![]() |
C.![]() |
D.![]() |
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