名校
解题方法
1 . 设抛物线
的焦点为
,准线为
,点
在抛物线上( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.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/01c74a907dda6bb7d9d56d009d9df253.png)
A.若直线![]() ![]() ![]() ![]() ![]() ![]() |
B.若直线![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若直线![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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2卷引用:广东省珠海市第二中学2021届高三6月数学试题
2 . 已知抛物线方程为
,直线
,点
为直线l上一动点,过点P作抛物线的两条切线,切点为A、B,则以下选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8605688eecca0f1f8d916657929bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
A.当![]() ![]() ![]() | B.直线![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
名校
解题方法
3 . 已知抛物线
的焦点
到其准线的距离为4,圆
,过
的直线
与抛物线
和圆
从上到下依次交于
四点,则
的最小值为_________ .
![](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/42103f88b80e7ef8bb12c7b839990a5f.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf810c8f387bbc753030c14e069d8d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b30fadc6a4933dc7588398687e3c8f4.png)
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6卷引用:广东省深圳市横岗高级中学2022届高三上学期9月第一次月考数学试题
(已下线)广东省深圳市横岗高级中学2022届高三上学期9月第一次月考数学试题江苏省盐城中学2021届高三下学期仿真模拟数学试题江苏省南京市第二十九中学2021-2022学年高三上学期期初第三次学情调研数学试题(已下线)专题25 圆锥曲线压轴小题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)河南省豫北名校2021-2022学年高二下学期5月调研考试理科数学试题江苏省扬州市新华中学2022-2023学年高二上学期期中数学试题
2021·浙江·模拟预测
4 . 如图,已知椭圆
与抛物线
,过椭圆下顶点
作直线
与抛物线交于
、
两点,且满足
,过点
作于直线
倾斜角互补的直线
交椭圆于
、
两点.
![](https://img.xkw.com/dksih/QBM/2021/5/21/2725927779696640/2725978904846336/STEM/576d9a48-75cc-4321-bc21-da714d467520.png?resizew=264)
(1)证明:点
的纵坐标为定值,并求出该定值;
(2)当
的面积最大时,求抛物线的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3cf706fe2ae0b2e99041ec1f4bf9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/8fb65b40aec32d52c7d1a18702604210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2021/5/21/2725927779696640/2725978904846336/STEM/576d9a48-75cc-4321-bc21-da714d467520.png?resizew=264)
(1)证明:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
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4卷引用:广东省中山市中山纪念中学2023-2024学年高二下学期二月份综合测练(开学考)数学试卷
5 . 已知抛物线
的焦点为
,直线
与抛物线C交于A,B两点.
(1)求
的面积;
(2)过抛物线C上一点Р作圆
的两条斜率都存在的切线,分别与抛物线C交于异于点P的两点D,E.证明:直线DE与圆M相切.
![](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/026808536f6b6d265c778e23836fbf13.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaceb8d6c6927e14d9ac7a557a2b11d.png)
(2)过抛物线C上一点Р作圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095c9f730b1d8c5eff9de7024a3474b3.png)
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|
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|
3卷引用:广东省茂名市2022届高三下学期调研(一)数学试题
解题方法
6 . 已知抛物线
的焦点为
,直线
过点
且与抛物线
交于
,
两点,分别过
,
两点作抛物线
的切线
,
,设直线
与
交于点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
___________ ,
面积的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.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/a0ed1ec316bc54c37c4286c208f55667.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/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/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/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53502463cc76201000e02df314e58769.png)
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|
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3卷引用:广东省2021届高三二模数学试题
广东省2021届高三二模数学试题(已下线)综合测试卷(巅峰版)-【新教材优创】突破满分数学之2020-2021学年高二数学课时训练(人教A版2019选择性必修第二册)江苏省连云港市灌南高级中学2022-2023学年高二上学期期中模拟数学试题
7 . 设
,
是抛物线
:
上两个不同的点,
为坐标原点,若直线
与
的斜率之积为-4,则下列结论正确的有( )
![](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/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
A.![]() | B.![]() |
C.直线![]() ![]() | D.![]() |
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3卷引用:广东省佛山市南海区西樵高级中学2021届高三下学期2月月考数学试题
19-20高二·全国·课后作业
名校
解题方法
8 . 已知
是过抛物线
的焦点
的直线
与抛物线
的交点,
是坐标原点,且满足
,
,则
的值为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.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/854a2086238ee12102a935ab38a2c43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8412aca18b64b4f767914c042e5c4c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/1f4439e3-8113-4acb-b91d-8b84f2265382.png?resizew=148)
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2020-12-12更新
|
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9卷引用:广东省2021届高三数学八省联考考前模拟仿真模拟卷
广东省2021届高三数学八省联考考前模拟仿真模拟卷(已下线)【新教材精创】3.3.2+抛物线的简单几何性质(2)-B提高练-人教A版高中数学选择性必修第一册(已下线)【新教材精创】2.7.2+抛物线的几何性质(2)-B提高练-人教B版高中数学选择性必修第一册(已下线)专题3.3 抛物线-《讲亮点》2021-2022学年高二数学新教材同步配套讲练(苏教版2019选择性必修第一册)(已下线)3.3.2 (整合练)抛物线的简单几何性质-2021-2022学年高二数学考点同步解读与训练(人教A版2019选择性必修第一册)(已下线)3.3.2 抛物线的几何性质(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)山东省部分校2021-2022学年高三下学期数学开学摸底考试试题山东省德州市第一中学2022-2023学年高二上学期1月期末数学试题四川省成都金苹果锦城第一中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
9 . 已知抛物线
:
(
)的焦点为
,准线为
,过
的直线交抛物线于
,
两点,作
,
,垂足分别为
,
,若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/0f85fca60a11e1af2bf50138d0e3fe62.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/e8e296c176f79b449f14ab19b527d473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/076056d278749c4cadf4b7cd08373f40.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/c5b7937d2541afc6351464650727a8fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2cc124ae4cbc5841b6fb86687aba619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
A.![]() | B.4 | C.5 | D.![]() |
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2020-12-02更新
|
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11卷引用:广东省2021届普通高中学业质量联合测评(11月大联考)高三数学试题
广东省2021届普通高中学业质量联合测评(11月大联考)高三数学试题河北省衡水中学2021届高三上学期学业质量联合测评数学试题(已下线)练习10+圆锥曲线的综合应用-2020-2021学年【补习教材·寒假作业】高二数学(理)(北师大版)(已下线)练习10+圆锥曲线的综合应用-2020-2021学年【补习教材·寒假作业】高二数学(文)(北师大版)(已下线)黄金卷01-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(新高考专用)2021年普通高等学校招生全国统一考试(全国2卷)冲刺卷(一)河北省玉田县第一中学2021届高三上学期12月段考数学试题江西省贵溪市第一中学2021-2022学年高二上学期第三次月考数学(理)试题河北省廊坊市第一中学2022-2023学年高二上学期11月月考数学试题广西壮族自治区钦州市第四中学2022-2023学年高二上学期10月月考数学试题(已下线)大招28抛物线结论荟萃
解题方法
10 . 如图所示,过抛物线
的焦点
作互相垂直的直线
,
,
交抛物线于
,
两点(
在
轴上方),
交抛物线于
,
两点,交其准线于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/fcb8032a-9752-410f-a33a-2bef39ba4422.png?resizew=268)
(1)求四边形
的面积的最小值;
(2)若直线
与
轴的交点为
,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/fcb8032a-9752-410f-a33a-2bef39ba4422.png?resizew=268)
(1)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
(2)若直线
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2020-11-23更新
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757次组卷
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7卷引用:黄金卷08(2024新题型)
(已下线)黄金卷08(2024新题型)中学生标准学术能力诊断性测试THUSSAT2021届高三诊断性测试 理科数学(一)试题(已下线)第十单元 计数原理(B卷 滚动提升检测)-2021年高考数学(理)一轮复习单元滚动双测卷(已下线)专题13 解析几何中的范围、最值和探索性问题 第一篇 热点、难点突破篇(练)-2021年高考数学二轮复习讲练测(浙江专用)(已下线)专题13 解析几何中的范围、最值和探索性问题(练)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(浙江专用)》(已下线)第11讲 高考难点突破三:圆锥曲线的综合问题(最值、范围问题) (精讲)(已下线)专题3.7 直线与抛物线的位置关系【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)