已知抛物线C:
上一点
与焦点F的距离为
.
(1)求
和p的值;
(2)直线l:
与C相交于A,B两点,求直线AM,BM的斜率之积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7585c7944d095b903c6e0d3dcbc228e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139e6e6c81a5c5f7179d855e0e977769.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
更新时间:2022-01-24 19:13:34
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【推荐1】已知F是抛物线C:的焦点,
是抛物线上一点,且
.
(1)求抛物线C的方程;
(2)直线l与抛物线C交于A,B两点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee808a07c981406a44a69cb124792071.png)
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【推荐2】已知抛物线
的焦点
,点
在抛物线
上.
(1)求
;
(2)过点
向
轴作垂线,垂足为
,过点
的直线
与抛物线
交于
两点,证明:
为直角三角形(
为坐标原点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8aed33984ccc91282d8a1c2be27cd0.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐1】抛物线具有光学性质:由其焦点射出的光线经抛物线反射后,沿平行于抛物线对称轴的方向射出;反之,平行于抛物线对称轴的入射光线经抛物线反射后必过抛物线的焦点.已知点
为抛物线
的焦点,
为坐标原点,
点在抛物线上,且其纵坐标为
,满足
.
(1)求抛物线
的标准方程;
(2)已知平行于
轴的光线
从点
射入,经过抛物线上的点
反射后,再经过抛物线上另一点
,最后沿
方向射出,若射线
平分
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d9223ae9c860bfb3d8427055ddd578.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知平行于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐2】设椭圆
,B为椭圆上任一点,F为椭圆左焦点,已知
的最小值与最大值之和为4,且离心率
,抛物线
的通径为4.
求椭圆和抛物线的方程;
设坐标原点为O,A为直线
与已知抛物线在第一象限内的交点,且有
.
试用k表示A,B两点坐标;
是否存在过A,B两点的直线l,使得线段AB的中点在y轴上?若存在,求出直线l的方程,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
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