解题方法
1 . 已知抛物线
的焦点为F,点P为抛物线上动点,点
为抛物线内的一个定点,已知
最小值为5.
(1)求抛物线E的标准方程;
(2)已知
的三个顶点都在抛物线E上,顶点
,
重心恰好是抛物线E的焦点F.求
所在的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643b31966f52a03f001f2e613cd701dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508734095955bb96d52f37be4e681700.png)
(1)求抛物线E的标准方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302e421a250119f34d8f3c9928730490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2 . 已知扡物线
的焦点为
,准线为
,过点
的直线交
于点
,与抛物线的一个交点为
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64447af8454c613a58b11d9274d3da2c.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/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/04ebd8c6f16984bd5a2127f75784d2a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
A.3 | B.6 | C.8 | D.12 |
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2023-02-23更新
|
143次组卷
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2卷引用:四川省乐山市2022-2023学年高二上学期期末数学理科试题
解题方法
3 . 已知抛物线
的焦点为F,过点F的直线交抛物线于A,B两点,分别过点A,B作准线的垂线,垂足分别记为
,
,若
,则
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37eac93736b605958ab6834b255dfa8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7c9fcfc78bd01e53151f8635072d28.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
4 . 已知F为抛物线
的焦点,直线
与C交于A,B两点(A在B的左边),则
的最小值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3348aa4cbf8f53e4ba7247acc94da5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6185e20fb073e5b281010573d6e121.png)
您最近一年使用:0次
名校
解题方法
5 . 已知点
,点B为直线
上的动点,过点B作直线
的垂线l,且线段
的中垂线与l交于点P.
(1)求点P的轨迹
的方程;
(2)设
与x轴交于点M,直线
与
交于点G(异于P),求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5421a28dc3675ae20190d6090793246e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319a01218514917e446dfc807a625ff.png)
(1)求点P的轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319a01218514917e446dfc807a625ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca797952ee1e84f43e1a7e80e6ff639.png)
您最近一年使用:0次
2023-02-25更新
|
731次组卷
|
3卷引用:四川省成都市第七中学2023-2024学年高二上学期期末复习数学试题(一)
四川省成都市第七中学2023-2024学年高二上学期期末复习数学试题(一)福建省厦门市2022-2023学年高二上学期期末考试数学试题(已下线)湖南省株洲市2023届高三下学期一模数学试题变式题17-22
名校
解题方法
6 . 已知斜率为
的直线
过抛物线
的焦点
,且被抛物线
所截得的弦
的长为
.
(1)求抛物线
的方程;
(2)求以抛物线
的准线与
轴的交点
为圆心,且与直线
相切的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求以抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-02-24更新
|
276次组卷
|
5卷引用:四川省绵阳南山中学实验学校2023-2024学年高二上学期期末模拟数学试题
名校
解题方法
7 . 已知直线
与抛物线
:
交于
,
两点,
为抛物线上一动点,
与线段
交于点
,且
,则
面积的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303094682b317daea83be885d1c7ff4b.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2e924f719c1b86910cad613c820e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
A.4 | B.6 | C.8 | D.10 |
您最近一年使用:0次
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解题方法
8 . 已知动点
到点
的距离等于它到直线
的距离,记动点
的轨迹为曲线
.
(1)求动点
的轨迹方程
;
(2)已知
,
,过点
的直线
与曲线
有且只有一个公共点
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cba284d675a3028d7a8d54f1f8ae70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
您最近一年使用:0次
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解题方法
9 . 已知动点M到点
的距离等于它到直线
的距离,记动点M的轨迹为曲线C.
(1)求动点M的轨迹方程C;
(2)已知
,过点
的直线l斜率存在且不为0,若l与曲线C有且只有一个公共点P,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
(1)求动点M的轨迹方程C;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cba284d675a3028d7a8d54f1f8ae70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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解题方法
10 . 已知抛物线
的顶点在原点,焦点坐标为
.
(1)求
的标准方程;
(2)若直线
与
交于
、
两点,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c30fd97fafb3779aa4f4660f41e2939.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-12-19更新
|
241次组卷
|
4卷引用: 四川省宜宾市南溪第一中学校2022-2023学年高二上学期期末模拟考试数学(理)试题
四川省宜宾市南溪第一中学校2022-2023学年高二上学期期末模拟考试数学(理)试题河南金太阳联考创新联盟2022-2023学年高二上学期11月第三次联考数学试题河南省驻马店市2022-2023学年高二上学期第三次联考数学试题(已下线)第09讲 拓展三:圆锥曲线的方程(弦长问题)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)