名校
解题方法
1 . 如图,已知抛物线
的焦点为F,点
为坐标原点,一条直线过定点
与抛物线相交于A,B两点,且
.
![](https://img.xkw.com/dksih/QBM/2022/8/22/3049791771590656/3052264560631808/STEM/3bf127a0886b462188ef324cb6ff89bf.png?resizew=147)
(1)求抛物线方程;
(2)连接AF,BF并延长交抛物线于C,D两点,求证:直线CD过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65368687df4d7e3b9304e85ec4de354c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://img.xkw.com/dksih/QBM/2022/8/22/3049791771590656/3052264560631808/STEM/3bf127a0886b462188ef324cb6ff89bf.png?resizew=147)
(1)求抛物线方程;
(2)连接AF,BF并延长交抛物线于C,D两点,求证:直线CD过定点
您最近一年使用:0次
2022-08-25更新
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661次组卷
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5卷引用:山西省太原市2022届高三第一次模拟数学(文)试题
名校
解题方法
2 . 已知
:
的焦点为
,斜率为
且经过点
的直线
与抛物线
交于点
,
两点(点
在第一象限),与抛物线的准线交于点
,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bbafa889700c6764ebc7fc1a42cd91.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() |
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2022-08-11更新
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596次组卷
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4卷引用:山西省山西大学附属中学2024届高三上学期9月月考(总第三次)数学试题
山西省山西大学附属中学2024届高三上学期9月月考(总第三次)数学试题(已下线)9.4 抛物线(精练)2023版 北师大版(2019) 选修第一册 突围者 第二章 全章综合检测(已下线)第20讲 抛物线定义及性质(2)
名校
解题方法
3 . 已知抛物线
:
的焦点为
,过点
且斜率为2的直线与抛物线
交于
,
两点(点
在
轴的上方),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52bb0f4140073a47e45c5093be46f1a9.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/a0ed1ec316bc54c37c4286c208f55667.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52bb0f4140073a47e45c5093be46f1a9.png)
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2022-05-31更新
|
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10卷引用:山西省部分学校大联考2023届高三上学期期末数学试题
山西省部分学校大联考2023届高三上学期期末数学试题山西省朔州市怀仁市第一中学校等学校2024届高三上学期摸底数学试题甘肃省庆阳市庆城县陇东中学2024届高三上学期第五次月考数学试题吉林省通化市梅河口市第五中学2024届高三三模数学试题河南省部分学校2021-2022学年高二5月联考理科数学试题河南省安阳市2021-2022学年高二下学期5月月考数学理科试题(已下线)第17讲 抛物线-【暑假自学课】2022年新高二数学暑假精品课(人教版2019必修第二册+选择性必修第一册)(已下线)第15讲 抛物线(1)四川省绵阳市南山中学实验学校2023-2024学年高二上学期期末模拟数学试题(五)黑龙江省大庆铁人中学2023-2024学年高二下学期开学考试数学试题
名校
解题方法
4 . 已知抛物线
上的点
与焦点
的距离为9,点
到
轴的距离为
.
(1)求抛物线
的方程.
(2)经过点
的直线与抛物线
交于
两点,
为直线
上任意一点,证明:直线
的斜率成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647da112824baed1f2bbfff103b748e8.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)经过点
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69609f8e3507a61acc52be28597d2cc3.png)
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2022-05-25更新
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9卷引用:山西省忻州市第一中学校2022届高三下学期5月模拟文科数学试题
解题方法
5 . 已知抛物线C开口向右,顶点为坐标原点,且经过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43433d049856933cfea2a3fcd033f26b.png)
(1)求抛物线C的方程;
(2)过点
的直线交抛物线C于点M,N,直线MA,NA分别交直线
于点P,Q,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43433d049856933cfea2a3fcd033f26b.png)
(1)求抛物线C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca54f085480b71c3bddb9a158611ec9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db2a853fd0a843772c7b112399a054b.png)
您最近一年使用:0次
6 . 已知抛物线
的焦点为F,M为T上一动点,N为圆
上一动点,
的最小值为
.
(1)求T的方程;
(2)直线l交T于A,B两点,交x轴的正半轴于点C,点D与C关于原点O对称,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3331494c6e0b32c275c259a2e0cb3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a58ff7a13f16152401ca349421cb3b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04af52c1e7a1317cdd43636ba705bf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4fdc034b4d20f15869d4c79b8161a0b.png)
(1)求T的方程;
(2)直线l交T于A,B两点,交x轴的正半轴于点C,点D与C关于原点O对称,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e839df5bcb6e835d21ffbdff727342b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85c44a34eebda86f1688b7d29b5557d.png)
您最近一年使用:0次
名校
解题方法
7 . 已知抛物线
:
的焦点为
,点
为
,若射线
与抛物线
相交于点
,与准线相交于点
,且
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b94c92959246552b816dc760170895.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/45e5cdcc3cf3ca21f12edaf5397ddbd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/784872651e6e5c6333bedde7fc6e1379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-05-09更新
|
534次组卷
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7卷引用:山西省晋中市2022届高三下学期5月模拟数学(文)试题
山西省晋中市2022届高三下学期5月模拟数学(文)试题山西省晋中市2022届高三下学期5月模拟数学(理科)试题山西省怀仁市第一中学校2022届高三下学期第四次模拟数学(理)试题山西省怀仁市第一中学校2022届高三下学期第四次模拟数学(文)试题甘肃省武威第一中学2022届高三文科数学冲刺试题(已下线)专题10 椭圆、双曲线与抛物线(已下线)3.3.1 抛物线的标准方程-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)
名校
解题方法
8 . 已知抛物线
与抛物线
在第一象限内的交点为
,若点
在圆
上,且直线
与圆
相切,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a59203badfd97c27a187b71dfcc3139.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9943617f89cb9a02d0fb233aa3f90b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a788754dde2c31d5eb02fae200aa100f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b103149e3f4ab2c5345be8aeab998a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a59203badfd97c27a187b71dfcc3139.png)
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2022-04-27更新
|
1153次组卷
|
5卷引用:山西省朔州市怀仁市第一中学2023届高三三模数学试题
山西省朔州市怀仁市第一中学2023届高三三模数学试题福建省2022届高三毕业班4月百校联合测评数学试题湖北省黄冈市蕲春县第一高级中学2022届高三下学期5月三模数学试题河北省衡水市2022届高三二模数学试题(已下线)考点22 抛物线-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)
9 . 已知抛物线
:
的焦点为F,C的准线与对称轴交于点D,过D的直线l与C交于A,B两点,且
,若FB为∠DFA的角平分线,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742d876b8c73235c7874847a7524a55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59e07e7f6425b2f93fe1e4f1295ee41.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-04-25更新
|
1311次组卷
|
4卷引用:山西省吕梁市交城县2022届高三核心模拟(下)理科数学(一)试题
山西省吕梁市交城县2022届高三核心模拟(下)理科数学(一)试题(已下线)考点8-4 抛物线及其性质(文理)(已下线)专题21 抛物线的焦点弦 微点2 抛物线的焦点弦常用结论及其应用综合训练河北省石家庄市正中实验中学2024届高三上学期月考(四)数学试题
10 . 设抛物线
:
的焦点为
,点
在
上,
,若以
为直径的圆过点
,则
的焦点到其准线的距离为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.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/532bcbe8307e6b2129bdcdbd553ee5f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2022-04-03更新
|
573次组卷
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3卷引用:山西省运城市高中联合体2022届高三下学期第四次模拟数学(理)试题