1 . 已知抛物线E的准线方程为:
,过焦点
的直线与抛物线
交于A、B两点,分别过A、B两点作抛物线
的切线,两条切线分别与
轴交于C、D两点,直线CF与抛物线
交于M、N两点,直线DF与抛物线
交于P、Q两点.
的标准方程;
(2)是否存在实数
,使得
恒成立,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cda91de2acdaeaa7f4942cf507ffbb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
2 . 过抛物线
的焦点
的直线
交抛物线
于
,
两点,若
,则线段
的中点到
轴距离为______ .
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/f1ed9d97b8745ed1c15349ea3fffc299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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解题方法
3 . 已知F为抛物线
的焦点,过点F的直线l与抛物线C相交于不同的两点A、B,若抛物线C在A、B两点处的切线相交于点P,则
的最小值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219cf0d81c1e04bb229185caac55339f.png)
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2024-04-24更新
|
357次组卷
|
2卷引用:四川省德阳市2024届高三下学期“三诊”考试(理科)数学试题
4 . 设抛物线
,过焦点
的直线与抛物线
交于点
、
.当直线
垂直于
轴时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/4aa9e607-413f-4aea-bdbc-427ada0cd9a0.png?resizew=164)
(1)求抛物线
的标准方程.
(2)已知点
,直线
、
分别与抛物线
交于点
、
.
①求证:直线
过定点;
②求
与
面积之和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544fc1ddf9f59d08c9feb5df9b4080d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e39fda3cda5ddc03b085413f2030aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/4aa9e607-413f-4aea-bdbc-427ada0cd9a0.png?resizew=164)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96499747e4aea990f4b878eea8d73ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.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)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
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2024-02-28更新
|
1068次组卷
|
4卷引用:四川省成都市成华区嘉祥外国语高级中学高2023-2024学年高二下学期3月月考数学试题
5 . 过抛物线
的焦点作直线l与C交于A,B两点,已知点
,若
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a42451bdbef6c82dbaf8e06f0614794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b768ea6a05cbf45b28fc46c501ba532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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解题方法
6 . 已知抛物线
的焦点为F,过点F的直线
交抛物线于M,N两点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.抛物线的焦点坐标是![]() |
B.焦点到准线的距离是4 |
C.![]() |
D.若点P的坐标为![]() ![]() |
您最近一年使用:0次
7 . 已如抛物线
的点为
,直线
与
交于
两点、则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4fb72e39d79b7a0cd892fa5fa34bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f6f1212ea1822365035920fa19e63c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
A.![]() ![]() ![]() |
B.若![]() ![]() |
C.设![]() ![]() ![]() |
D.过![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-01-24更新
|
142次组卷
|
2卷引用:四川省宜宾市普通高中2023-2024学年高二上学期学业质量监测数学试卷
解题方法
8 . 在直角坐标系
中,已知点
,直线
,过
外一点
作
的垂线,垂足为
,且
,记动点
的轨迹为
,过点
作
的切线,该切线与
轴分别交于
两个不同的点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/03aef004-0438-47de-9cb8-75208d5b6211.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f363d815fde5c34c317df8c6a1d616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4180dae966f648d368a10edf3b7e3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/d2c9713f21c1af0d7c4579ab6fd56bd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/03aef004-0438-47de-9cb8-75208d5b6211.png?resizew=170)
A.动点![]() ![]() |
B.当![]() ![]() |
C.对任意点![]() ![]() ![]() |
D.设![]() ![]() |
您最近一年使用:0次
2024-01-17更新
|
279次组卷
|
3卷引用:四川省眉山市仁寿县两校2023-2024学年高二下学期开学联考数学试题
9 . 抛物线的弦与过弦的端点的两条切线所围成的三角形常被称为阿基米德三角形,该三角形以其深刻的背景、丰富的性质产生了无穷的魅力.设抛物线
(
),弦
过焦点
,
为其阿基米德三角形,则下列结论一定成立的是( )
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
A.点![]() ![]() ![]() ![]() |
B.存在点![]() ![]() |
C.![]() |
D.![]() ![]() |
您最近一年使用:0次
解题方法
10 . 已知抛物线
的焦点为
.
(1)已知过点
的直线
与抛物线
相交于
两点,求证:以
为直径的圆与直线
相切;
(2)若直线
交抛物线
于
两点,当
的面积为2时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35eb39164fe9ef2dbf88982cbf0a3974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adccd1dd14171c8c29d4a3836728c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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