1 . 设抛物线
,过焦点
的直线与抛物线
交于点
、
.当直线
垂直于
轴时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/4aa9e607-413f-4aea-bdbc-427ada0cd9a0.png?resizew=164)
(1)求抛物线
的标准方程.
(2)已知点
,直线
、
分别与抛物线
交于点
、
.
①求证:直线
过定点;
②求
与
面积之和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544fc1ddf9f59d08c9feb5df9b4080d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.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/08e39fda3cda5ddc03b085413f2030aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/4aa9e607-413f-4aea-bdbc-427ada0cd9a0.png?resizew=164)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96499747e4aea990f4b878eea8d73ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
您最近一年使用:0次
2024-02-28更新
|
1068次组卷
|
4卷引用:江西省红色十校2024届高三下学期2月联考数学试卷
解题方法
2 . 设抛物线
的焦点为
,过
点的直线与
交于
两点,
.
(1)求抛物线
的方程;
(2)
为
上异于
的任意一点,直线
分别与
的准线相交于
两点,证明:以线段
为直径的圆经过
轴上的两个定点.
![](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/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/cce30ab9a6c94b688272c00f89b72db1.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
解题方法
3 . 已知抛物线
的焦点为F,抛物线H上的一点M的横坐标为5,
为坐标原点,
.
(1)求抛物线H的方程;
(2)若一直线经过抛物线H的焦点F,与抛物线H交于A,B两点,点C为直线
上的动点.
①求证:
.
②是否存在这样的点C,使得△ABC为正三角形?若存在,求点C的坐标;若不存在,说明理由,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97ac4bc0ad26a4cc50b0e38596ef04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a354e98b6eb10e0c8463ae03e559b63.png)
(1)求抛物线H的方程;
(2)若一直线经过抛物线H的焦点F,与抛物线H交于A,B两点,点C为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f16491db019b0e1f9d1f23409242fd.png)
②是否存在这样的点C,使得△ABC为正三角形?若存在,求点C的坐标;若不存在,说明理由,
您最近一年使用:0次
2022-05-11更新
|
1197次组卷
|
3卷引用:山东省临沂市2022届高三二模考试数学试题
解题方法
4 . 过抛物线
焦点F的直线l交抛物线于点A、B,弦
长的最小值为4,直线
分别交直线
于点C,D(O为原点)·
![](https://img.xkw.com/dksih/QBM/2022/3/16/2937539728515072/2938915943669760/STEM/53a33ab18a5842349d03fbdf3330808a.png?resizew=189)
(1)求抛物线E的方程;
(2)圆M过点C、D,交x轴于点
,证明:若t为定值时,m也为定值.并求
时
面积S的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3562ca8ceed66136350983b2c9caf83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d6f2327f2fb63777d199e0d75f9539.png)
![](https://img.xkw.com/dksih/QBM/2022/3/16/2937539728515072/2938915943669760/STEM/53a33ab18a5842349d03fbdf3330808a.png?resizew=189)
(1)求抛物线E的方程;
(2)圆M过点C、D,交x轴于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc60d731a5d0640ec1119e42f75dff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473239f6bac88262276d3a7cc6d6b31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/370abdf35cb8817d35b78eea892731ce.png)
您最近一年使用:0次
5 . 已知抛物线
的焦点为F,以F和准线上的两点为顶点的三角形是边长为
的等边三角形,过
的直线交抛物线E于A,B两点.
(1)求抛物线E的方程;
(2)是否存在常数
,使得
,如果存在,求
的值,如果不存在,请说明理由;
(3)证明:
内切圆的面积小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c42d88e496a17562d25195301e0ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83dbfddc6f98548699ed581e8c8608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ab82c33e6c1f8b73628fa78e6868b4.png)
(1)求抛物线E的方程;
(2)是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33104cb3b15fa0e01842e78f9ed59701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
您最近一年使用:0次
2022-02-13更新
|
433次组卷
|
3卷引用:山东省菏泽市2021-2022学年高二上学期期末数学试题
2011·北京西城·一模
6 . 已知抛物线
的焦点为
,过
的直线交
轴正半轴于点
,交抛物线于
两点,其中点
在第一象限.
(Ⅰ)求证:以线段
为直径的圆与
轴相切;
(Ⅱ)若
,
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b3932717847eb0859019f07a7445ab.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅰ)求证:以线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93dd4d854fbc236bccbd97a5d715fe97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1266096a1e8b8de08172b4ebc9d19659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3018c41828a4dae13bc106a973f61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23afe274ce13cdca597f9e1144181c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f31e2188a6843eea5270500ec4bd1fa.png)
您最近一年使用:0次