名校
1 . 已知抛物线
,p为方程
的根.
(1)求抛物线的方程;
(2)若抛物线与直线
无公共点,求此抛物线的通径
(通径:过抛物线的焦点且与对称轴垂直的直线被抛物线所截得的线段).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffa6a8471c126c4c6b789490d84144b.png)
(1)求抛物线的方程;
(2)若抛物线与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daab03b1642f1ea187c94f62088ac0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
您最近一年使用:0次
2 . 已知曲线
和定点
,点
为曲线
上任意一点,若
,当点
在曲线
上运动时,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8366446007f5e9a1e28ba3ae7cfea23e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50edfb9ed0d50d6f35ad6a130208d307.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/bbe51a2c12e6f14dea578d8adf9f81fd.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/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
3 . 已知顶点在原点,焦点在
轴上的抛物线被直线
截得的弦长为
,求该抛物线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6342e0a5a8942cfb1cf535ceb2c50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b12efb03327f461e868b2ea433f9b0.png)
您最近一年使用:0次
23-24高二上·全国·课后作业
4 . 已知
为坐标原点,
为抛物线
的焦点,
为
上一点,若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05335b4876c7a2e53172fe811c51579.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/527ac6e1d3ee58fe2e06cad33731cd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c71c49dc9a9de1a0221769e4eb8616.png)
您最近一年使用:0次
5 . 已知
是抛物线
的焦点,
是
上一点,
的延长线交
轴于点
.若
为
的中点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.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/2273ae1ee99cec9c1304323bc9ebf75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1460aa3d83df61f6c411b34412135451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01dd40db0d70d501f4c06ecebd8de702.png)
您最近一年使用:0次
6 . 填空:
(1)设抛物线
上一点P到y轴的距离是4,则点P到该抛物线焦点的距离为___________ ;
(2)设抛物线
上一点M到焦点的距离为1,则点M的坐标为___________ .
(1)设抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
(2)设抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1183df9f26985febdc844cda75ed4c.png)
您最近一年使用:0次
23-24高二上·全国·课后作业
解题方法
7 . 求适合下列条件的抛物线的标准方程:
(1)顶点在原点,准线方程为
;
(2)顶点在原点,且过点
;
(3)顶点在原点,对称轴为x轴,焦点在直线
上;
(4)焦点在x轴上,且抛物线上一点
到焦点的距离为5.
(1)顶点在原点,准线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de72a5190834f5dbe895596656c038b3.png)
(2)顶点在原点,且过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bad9a4a9365dc43f23c27b9a64426a3.png)
(3)顶点在原点,对称轴为x轴,焦点在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff1b89e2b6f0b3243afe3c936b8b407.png)
(4)焦点在x轴上,且抛物线上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651c4b1b8f1f54f0af97107020acf253.png)
您最近一年使用:0次
2023-09-11更新
|
969次组卷
|
9卷引用:3.3 抛物线
(已下线)3.3 抛物线(已下线)3.3.1 抛物线及其标准方程(分层练习)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第一册)(已下线)高二上学期期中复习【第三章 圆锥曲线的方程】十大题型归纳(基础篇)-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)湘教版(2019)选择性必修第一册课本习题 习题3.3(已下线)第03讲 3.3抛物线(8大题型训练)-【练透核心考点】2023-2024学年高二数学上学期重点题型方法与技巧(人教A版2019选择性必修第一册)(已下线)3.3.1 抛物线的标准方程(五大题型)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)(已下线)专题26 抛物线及其标准方程5种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)(已下线)专题3.3 抛物线(6个考点十大题型)(1)(已下线)通关练17 抛物线8考点精练(1)
23-24高二上·全国·课后作业
8 . 求下列抛物线的焦点坐标和准线方程:
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1704032413ac0663ac1575484aa00ab8.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644c98e1cbfed85087f73693733cb950.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb3b9aab72de273ba2f38c9624e94ba.png)
您最近一年使用:0次
23-24高二上·全国·课后作业
9 . 在同一坐标系中画出下列抛物线:再比较这些图形,说明抛物线开口的大小与方程中x的系数之间的关系.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f703f111d182756d24b366439a4b1eb8.png)
(2)
;
(3)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f703f111d182756d24b366439a4b1eb8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
您最近一年使用:0次
23-24高二上·全国·课后作业
10 . 求下列抛物线的顶点坐标、对称轴、焦点坐标和准线方程.
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d957c80c140881b077f0c45dce2d69.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de93f6c82dd81b3e52079ff72e998969.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87c12a36789ea43bea2f0f66689a4f0.png)
您最近一年使用:0次