1 . 过抛物线
的焦点F作斜率分别为
的两条不同的直线
,且
,
相交于点A,B,
相交于点C,D.以AB,CD为直径的圆M,圆N(M,N为圆心)的公共弦所在的直线记为
.
(I)若
,证明;
;
(II)若点M到直线
的距离的最小值为
,求抛物线E的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a69ab234c3a8a40a9d0a9620df498af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec7bcf5820dfe70290259c2d7ac1ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe42865a8ca3fe91e104273a4174e079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46fbee1091c01d2752d3ec2e804bf9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(I)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90931781b834d100def5e571c28486db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc119913022c0911844ab30307982a41.png)
(II)若点M到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97814cbb7a07b2e5726d144f97ebf444.png)
您最近一年使用:0次
2016-12-02更新
|
3129次组卷
|
3卷引用:2013年全国普通高等学校招生统一考试理科数学(湖南卷)
真题
解题方法
2 . 定长为3的线段AB的两端点在抛物线
上移动,记线段AB的中点为M,求点M到y轴的最短距离,并求此时点M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
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真题
解题方法
3 . 已知点
,
是抛物线
上的两个动点,
是坐标原点,向量
,
满足
.设圆
的方程为
.
(1)证明线段
是圆
的直径;
(2)当圆
的圆心到直线
的距离的最小值为
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75893f778061c3a7270f02db57fba2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588414d07bcedbf1e7d46d0d028e269d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5773af927ab0caa208eef1adf9e87aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbfd7bfa201296e1797635f02240835b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dd85a205ad4f52154f0141f45b8f6c.png)
(1)证明线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2020-06-26更新
|
367次组卷
|
3卷引用:2006 年普通高等学校招生考试数学(文)试题(辽宁卷)
4 . 已知直线
;圆
;抛物线
.又L与M交于点A,B;L与
交于点C,D.求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b49df89bb477a31dba5dfab1b5c9039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cfb810cc41812c9f6c4ec3fe7aa3c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595605b6d3da4e255b65877776903402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af455ec9bf77300245a80e74d718dec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21efbd352506e29415d0794157a605e3.png)
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真题
5 . 过点
的直线
与抛物线
交于
、
两点.记:线段
的中点为
;过点
和这个抛物线的焦点
的直线为
;
的斜率为
.试把直线
的斜率与直线
的斜率之比表示为
的函数,并指出这个函数的定义域、单调区间,同时说明在每一单调区间上它是增函数还是减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c8c934fb978c8840bed9680408977c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd49bf20f987c05b4d36e31549075c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd49bf20f987c05b4d36e31549075c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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真题
解题方法
6 . 如图,在平面直角坐标系
中,过
轴正方向上一点
任作一直线,与抛物线
相交于
两点,一条垂直于
轴的直线,分别与线段
和直线
交于
,
,
(1)若
,求
的值;
(2)若
为线段
的中点,求证:
为此抛物线的切线;
(3)试问(2)的逆命题是否成立?说明理由.
![](https://img.xkw.com/dksih/QBM/2011/6/17/1570243585253376/1570243590774784/STEM/51d6f973-78e3-4c0f-ad4f-1ee36220851a.png?resizew=199)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40aaa43c219bd035f09cc00cf3e15071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca820a22ae8c1223ec6a7b8c89bf768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22905409f038387f0e954a47384b60a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
(3)试问(2)的逆命题是否成立?说明理由.
![](https://img.xkw.com/dksih/QBM/2011/6/17/1570243585253376/1570243590774784/STEM/51d6f973-78e3-4c0f-ad4f-1ee36220851a.png?resizew=199)
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