名校
解题方法
1 . 已知抛物线
,过点
的直线
与
交于不同的两点
.当直线
的倾斜角为
时,
.
(1)求
的方程;
(2)在线段
上取异于点
的点
,且满足
,试问是否存在一条定直线,使得点
恒在这条定直线上?若存在,求出该直线;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4771434a43ef4202325593a9d6931abb.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0244675766f73552e4712660cf4cb7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a652cc046b70eca012a2121ccff9740.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa86243cf565317dedc9fee91956cab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
今日更新
|
74次组卷
|
2卷引用:2024届湖南省长沙市第一中学高考最后一卷数学试题
名校
解题方法
2 . 已知抛物线
的顶点是椭圆
的中心,焦点与该椭圆的右焦点重合.
(1)求抛物线
的方程;
(2)已知动直线
过点
,交抛物线
于
、
两点,坐标原点
为
中点,
①求证:
;
②是否存在垂直于
轴的直线
被以
为直径的圆所截得的弦长恒为定值?如果存在,求出
的方程;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b7421c2552d1b5e172cbe498b571ff.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)已知动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af74113f38fffeed8075e57d7f9d2533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba069fd3d0a8244e67f42c73e255d52f.png)
②是否存在垂直于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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7日内更新
|
91次组卷
|
3卷引用:专题4 抛物线切线与阿基米德三角形【练】(压轴题大全)
(已下线)专题4 抛物线切线与阿基米德三角形【练】(压轴题大全)河北省秦皇岛市新世纪高级中学2023-2024学年高二下学期开学考试数学试卷黑龙江省哈尔滨市第九中学校2023-2024学年高二下学期期中考试数学学科试卷
名校
3 . 已知抛物线
的焦点为F,过点
的直线l与
交于A、B两点.设
在点A、B处的切线分别为
,
,
与x轴交于点M,
与x轴交于点N,设
与
的交点为P.
的斜率,并证明
;
(2)证明:点P必在直线
上;
(3)若P、M、N、T四点共圆,求点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179234a7f5454002d6519079a5ff7972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4244ff1376012b8dd673587e9ffdffef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/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/14b5aed438b6ff97ebcb449fc80fa431.png)
(2)证明:点P必在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
(3)若P、M、N、T四点共圆,求点P的坐标.
您最近一年使用:0次
名校
解题方法
4 . 已知曲线
的方程为
,过
作直线与曲线
分别交于
两点.过
作曲线
的切线,设切线的交点为
.则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128aa322f3e76e8f03a7402bb2b2ae25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089535b1341bfc25dd0471ca0d7b90b2.png)
您最近一年使用:0次
解题方法
5 . 已知抛物线
的焦点为F,过F的直线l与C交于A,B两点,点P在C的准线上,那么( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
A.若PA与C相切,则PB也与C相切 |
B.![]() |
C.若点P在x轴上,则![]() |
D.若点P在x轴上,且满足![]() ![]() |
您最近一年使用:0次
6 . 已知抛物线
的焦点为
,过
作互相垂直的直线
,分别与
交于
和
两点(A,D在第一象限),当直线
的倾斜角等于
时,四边形
的面积为
.
(1)求C的方程;
(2)设直线AD与BE交于点Q,证明:点
在定直线上.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/f65adb9d8969b8d885e9c7d53746a90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945e93c9f3515ded840de09a9ba81ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814397354c2ae1cb08e0271305970811.png)
(1)求C的方程;
(2)设直线AD与BE交于点Q,证明:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
解题方法
7 . 已知抛物线
的焦点为
,过
的直线
与
交于
两点,点
在第一象限内,点
在
的准线上,则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.若![]() ![]() ![]() ![]() |
B.![]() |
C.若点![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
8 . 已知抛物线
,过点
的直线与抛物线
交于
两点,设抛物线
在点
处的切线分别为
和
,已知
与
轴交于点
与
轴交于点
,设
与
的交点为
.
(1)证明:点
在定直线上;
(2)若
面积为
,求点
的坐标;
(3)若
四点共圆,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d094a0415fd4c9639f5950a3b522d77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93f320cfddc8ea21099f8e4892ddd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e95f7197eefaa30c63b73aef5ef464b.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)证明:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172949380786d26b89d4ddd7850f3af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-04-26更新
|
2076次组卷
|
4卷引用:湖北省武汉市2024届高三下学期四月调考数学试卷
湖北省武汉市2024届高三下学期四月调考数学试卷(已下线)第6题 设点or设线解决阿基米德三角形问题(压轴大题)山东省日照市五莲县第一中学2024届高考模拟预测(一)数学试题(已下线)专题4 抛物线切线与阿基米德三角形【讲】(压轴题大全)
9 . 已知抛物线Γ:
,过点
作直线
,直线
与Γ交于A,C两点,A在x轴上方,直线
与Γ交于B,D 两点,D在x轴上方,连接
,若直线
过点
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290a56449ad6dd65aec7525c94273f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57901924f7747648bcaca87f0bf9915d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/2d54c40e77fc6b5d018e5d1ab271c450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
A.若直线![]() ![]() ![]() |
B.直线![]() ![]() |
C.直线![]() ![]() ![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
10 . 已知点
,
,
和动点
满足
是
,
的等差中项.
(1)求
点的轨迹方程;
(2)设
点的轨迹为曲线
按向量
平移后得到曲线
,曲线
上不同的两点M,N的连线交
轴于点
,如果
(
为坐标原点)为锐角,求实数
的取值范围;
(3)在(2)的条件下,如果
时,曲线
在点
和
处的切线的交点为
,求证:
在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b54b9cf95418bc3dce6e4c698b9907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3752eaf8b6f65d3faf930dc54bf2ef1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a476588acbf41d798cc234a52fa21a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7aaa871ceb78e5b80b531a7cf4f1c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22bd33096120ddae671fb7952f3f534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a981fb29b651cfdbd60c30b9781773c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27935c1ef4df2d52ac697678a3c8f39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)在(2)的条件下,如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
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