解题方法
1 . 已知抛物线
:
(
)的焦点为
,过焦点
作直线
交抛物线
于
两点,
为抛物线
上的动点,且
的最小值为1.
(1)抛物线
的方程;
(2)若直线
交抛物线
的准线于点
,求线段
的中点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/a7f20bf927d76ca5c9679922cc89f489.png)
(1)抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9446ea29ddb6650a5a0cf7ac6f17d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2 . 已知抛物线
的焦点为
,
,
,
为
上不重合的三点.
(1)若
,求
的值;
(2)过
,
两点分别作
的切线
,
,
与
相交于点
,过
,
两点分别作
,
的垂线
,
,
与
相交于点
.
(i)若
,求
面积的最大值;
(ii)若直线
过点
,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32be681ecfdd5463567671d1ee034d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d856ed2306a7cc3e64a1edfb84627aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6740760f007759d12ab009808527bb.png)
(2)过
![](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/2a30f3a8b673cc28bd90c50cf1a35281.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/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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
(ii)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
解题方法
3 . 已知椭圆
的左、右焦点分别为
,抛物线
以
为焦点,过
的直线
交抛物线
于
两点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/8e3a1467ecf286e3cadaf5aa006606f2.png)
A.若![]() ![]() | B.当![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() | D.![]() |
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F,直线l交抛物线T于A,B两点,M为线段
的中点,过点M作抛物线T的准线的垂线,垂足为N,若
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a79fb62bf112c4a8be625548db0ea92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7045662503f0cacd7736523f5ec928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c683d0f5034025be78bb6be865c8368a.png)
A.1 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-22更新
|
862次组卷
|
2卷引用:贵州省安顺市第二高级中学2023-2024学年高三下学期第一次模拟考试数学试题
名校
解题方法
5 . 设抛物线
的焦点为
,点
为该抛物线上任意一点,若
恒成立,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae230f36b56a831b03ffb2cde1b27cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知
为坐标原点,
为抛物线
上两点,
为
的焦点,若
到准线
的距离为2,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.若![]() ![]() ![]() |
B.若直线![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2024-03-04更新
|
505次组卷
|
3卷引用:贵州省黔东南苗族侗族自治州2023-2024学年高三上学期九校联考(开学考)数学试题
名校
7 . 已知直线与抛物线
交于
,
两点,抛物线的焦点为
,
为原点,且
,
于点
,点
的坐标为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248f9bb8dd23ab0fa70e774678d91641.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff943294f05b35ff92e559fa7dc891bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cee097d4fe948c3d4f1b5c28b24adf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f48e1c656aace41360467f254e359d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248f9bb8dd23ab0fa70e774678d91641.png)
您最近一年使用:0次
名校
8 . 已知抛物线
的焦点为
,准线为
,点
在抛物线
上,过
作
的垂线,垂足为
,若
(
为坐标原点),则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.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/bfa2c333eb3a718785c053a900c10d9a.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e430de9d088494fae303e65baf93a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd29b2e8192d673308bdf8d5cb6cab.png)
A.5 | B.2 | C.![]() | D.![]() |
您最近一年使用:0次
2023-11-29更新
|
483次组卷
|
2卷引用:贵州省黔东南州九校2024届高三上学期11月月考数学试题
名校
9 . 设P为抛物线C:
上的动点,
关于P的对称点为B,记P到直线
的距离分别
,
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de20ed223a7b6a32f4a91a856e699f87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7a537b990b2531787e34356757f3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414835f8dfd13fdea54d575aae996322.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-05-25更新
|
1380次组卷
|
14卷引用:贵州省凯里市第一中学2023届高三高考模拟预测数学(理)试题
贵州省凯里市第一中学2023届高三高考模拟预测数学(理)试题贵州省凯里市第一中学2023届高三模拟考试数学(文)试题湖北省孝感市重点中学2023届高三下学期5月最后一卷数学试题河南省名校联考2023届高三5月最终模拟文科数学试题河南省名校联考2023届高三下学期5月模拟理科数学试题江西省稳派联考2023届高三模拟预测数学(理)试题江西省稳派联考2023届高三模拟预测数学(文)试题河北省沧州市示范性高中2023届高三三模数学试题(已下线)热点7-4 抛物线及其应用(6题型+满分技巧+限时检测)(已下线)专题3.6 抛物线的标准方程和性质【八大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)3.3 抛物线(精练)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)(已下线)专题09 抛物线综合性质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08 抛物线的压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)(已下线)3.3.1 抛物线及其标准方程(5大题型)精练-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)
名校
10 . 已知抛物线
的焦点为
,准线
与坐标轴交于点
是抛物线上一点,若
,则
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.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/be452c8bdea6b4e4c7a6d96e9dc6a51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1102626e3c8090cb2e8aa319c97927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfb02e157819a2bdd0f2790cbc825e9.png)
A.4 | B.![]() | C.![]() | D.2 |
您最近一年使用:0次
2023-05-08更新
|
1947次组卷
|
10卷引用:贵州省部分高中2023届高三模拟考试数学(文)试题