1 . 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![]() ![]() ![]() ![]() |
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2024-01-24更新
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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
名校
解题方法
2 . 已知拋物线
的焦点为
,过点
且斜率为
的直线
交
于
两点.当
时,
.
(1)求
的方程;
(2)若
关于
轴的对称点为
,当
变化时,求证:直线
过定点,并求该定点坐标.
![](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/f0a532e15e232cb4b99a8d4d07c89575.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e041a52887466723ea61f8a373185218.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e733a15f50fdde9ac81ac1ce6e863f.png)
您最近一年使用:0次
2022-07-20更新
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284次组卷
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5卷引用:四川省资阳市2021-2022学年高二下学期期末质量检测数学(理)试题
四川省资阳市2021-2022学年高二下学期期末质量检测数学(理)试题四川省资阳市2021-2022学年高二下学期期末数学文科试题四川省泸县第四中学2022-2023学年高二下学期开学考试数学(理)试题江苏省南京外国语学校2023-2024学年高二上学期10月月考数学试题(已下线)专题3-6 抛物线综合大题归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)
名校
3 . 给出下列命题:
①直线
的倾斜角是
;
②已知过抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
的焦点
的直线与抛物线
交于
,
两点,则有
;
③已知
、
为双曲线
:
的左、右焦点,点
为双曲线右支上异于顶点的任意一点,则
的内心
始终在一条直线上.
其中所有正确命题的序号为___________ .
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7347b88954b4a322f82c38a6af61e5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
②已知过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/464317f356a60f01538cae5336bb136b.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709dd83332fdd081a71c83c83215ecf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
其中所有正确命题的序号为
您最近一年使用:0次
2016-12-03更新
|
1815次组卷
|
4卷引用:2015-2016学年四川绵阳南山中学高二上期中理科数学试卷
2015-2016学年四川绵阳南山中学高二上期中理科数学试卷四川省绵阳市南山中学实验学校2016-2017学年高二上学期半期考试数学(理)试题2015-2016学年辽宁省葫芦岛市一中高二上期中理科数学卷(已下线)专题27 圆锥曲线与四心问题 微点5 圆锥曲线与四心问题综合训练
4 . 过抛物线C:y2=2px(p>0)的焦点F作斜率为
的直线l与C及其准线分别相交于A,B,D三点,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9f91286d35d6d9806727dec4536aad.png)
A.2或![]() | B.3或![]() | C.1 | D.4或![]() |
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2020-03-29更新
|
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5卷引用:四川省泸州市2017届高三四诊(临考冲刺模拟)数学(理)试题
四川省泸州市2017届高三四诊(临考冲刺模拟)数学(理)试题2020届四川省宜宾市叙州区第二中学校高三三诊模拟考试数学(理)试题2020届四川省宜宾市叙州区第二中学校高三三诊模拟考试数学(文)试题2020届陕西省西安中学高三下学期第三次模拟考试数学(理)试题(已下线)专题05 解析几何(第一篇)-备战2020高考数学黄金30题系列之压轴题(新课标版)
名校
5 . 设抛物线
(
)的焦点为
,准线为
.过焦点的直线分别交抛物线于
两点,分别过
作
的垂线,垂足为
. 若
,且三角形
的面积为
,则
的值为___________ .
![](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/01c74a907dda6bb7d9d56d009d9df253.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/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f8f333303816ff66e3aa44bcf97268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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710次组卷
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4卷引用:四川省成都市新都区成都外国语学校高新校区2019-2020学年高二上学期期中数学试题
6 . 已知抛物线
:
的焦点为
,
为
上的动点,直线
与
的另一交点为
,
关于点
的对称点为
.当
的值最小时,直线
的方程为_______ .
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61f62c429fbc1e76dd155bc174e9ed0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c422f948a3355ff742cc782b1f9fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
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名校
解题方法
7 . 倾斜角为锐角
的直线过抛物线
的焦点,与抛物线交于
、
两点,线段
的垂直平分线与
轴交于点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec6e6ee5ffa5a1a447e630b0d092ee4.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec6e6ee5ffa5a1a447e630b0d092ee4.png)
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8 . 已知抛物线y2=2px(p>0)的焦点为F,过F且与x轴垂直的直线交该抛物线于A,B两点,|AB|=4.
(1)求抛物线的方程;
(2)过点F的直线l交抛物线于P,Q两点,若△OPQ的面积为4,求直线l的斜率(其中O为坐标原点).
(1)求抛物线的方程;
(2)过点F的直线l交抛物线于P,Q两点,若△OPQ的面积为4,求直线l的斜率(其中O为坐标原点).
您最近一年使用:0次
2019-01-02更新
|
632次组卷
|
7卷引用:四川省泸州市泸县第一中学2022-2023学年高二下学期开学考试数学(理)试题
9 . 如图,过抛物线
的焦点
作倾斜角为
的直线
,
与抛物线及其准线从上到下依次交于
、
、
点,令
,
,则当
时,
的值为
![](https://img.xkw.com/dksih/QBM/2018/3/28/1911761178984448/1912396312641536/STEM/74eb8ac664d6447cb2ab596eea19cd47.png?resizew=159)
![](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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/ab83a9d23509473b740374ac4f764eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7964a5a6496f81a4a97563d8c8e4aa75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e2c8d466ab8eb5ecd38060b53bbe8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
![](https://img.xkw.com/dksih/QBM/2018/3/28/1911761178984448/1912396312641536/STEM/74eb8ac664d6447cb2ab596eea19cd47.png?resizew=159)
A.3 | B.4 | C.5 | D.6 |
您最近一年使用:0次
2018-03-29更新
|
797次组卷
|
3卷引用:四川省德阳市2018届高三二诊考试文科数学试题
名校
解题方法
10 . 已知O是坐标原点,抛物线
的焦点为F,过F且斜率为1的直线交抛物线C于A,B两点,Q为抛物线C的准线上一点,且
.
(1)求Q点的坐标;
(2)设与直线垂直的直线与抛物线C交于M,N两点,过M,N分别作抛物线C的切线
,
设直线
与
交于点P,若
,求
外接圆的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb9603390e28948abd2e3cd96e1720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8f9831e15ff7343d5146e9602a21b8.png)
(1)求Q点的坐标;
(2)设与直线垂直的直线与抛物线C交于M,N两点,过M,N分别作抛物线C的切线
![](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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
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2020-03-25更新
|
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5卷引用:四川省成都市双流中学2018-2019学年高二下学期6月月考数学(理)试题
四川省成都市双流中学2018-2019学年高二下学期6月月考数学(理)试题【省级联考】云南省2019届高三第二次复习统一检测文科数学试题【省级联考】云南省2019届高三第二次高中毕业生复习统一检测理科数学试题(已下线)重难点11九种直线和圆的方程的解题方法-3(已下线)第20题 抛物线焦点弦、切线方程问题(压轴小题)