已知直线l与抛物线C:y2=4x交于A,B两点,M(2,y0)(y0≠0)为弦AB的中点,过M作AB的垂线交x轴于点P
(1)求点P的坐标;
(2)当弦AB最长时,求直线l的方程.
(1)求点P的坐标;
(2)当弦AB最长时,求直线l的方程.
更新时间:2020-03-01 11:33:28
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【知识点】 直线与抛物线相交求直线方程
相似题推荐
【推荐1】已知抛物线
和
:
,过抛物线上的一点
,作
的两条切线,与
轴分别相交于
,
两点.
![](https://img.xkw.com/dksih/QBM/2018/4/21/1928836928397312/1932993497251840/STEM/2ef8a3f7671944879db9de706fd25fab.png?resizew=248)
(Ⅰ)若切线
过抛物线的焦点,求直线
斜率;
(Ⅱ)求面积
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecfe932bf546c53654f7ec2cc80019c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2018/4/21/1928836928397312/1932993497251840/STEM/2ef8a3f7671944879db9de706fd25fab.png?resizew=248)
(Ⅰ)若切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(Ⅱ)求面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2694c32ca1e120e988012b7ecd74f625.png)
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解答题-问答题
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适中
(0.65)
【推荐2】已知抛物线
的焦点为F,过点
作倾斜角为
的直线交抛物线
于A,B两点,且
.
(1)求抛物线
的方程;
(2)直线l的方程为
,且直线l与抛物线
相交于C,D两点,若以
为直径的圆E恰好经过点F,求圆E的半径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d76978ae010877e6b8280f2a133333cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15677a5ee41c77919ebf114b646ec88c.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)直线l的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7da20c17eab842b24d5cd20dd37b77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次