1 . 在平面直角坐标系
中,已知动圆
经过定点
且与直线
相切,记动圆
的圆心
的轨迹为曲线
.
(1)求曲线
的方程;
(2)设直线
与曲线
相交于
、
两点,
为坐标原点,
、
的斜率分别为
,
,且满足
,
的面积为8,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2347bec7975dab2b8bce2fd19b1237d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6e582064c4754d7c4dfd51645aadb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80065003fe6677e9a6b4f0dfb9d1db0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4f28029c21c82a381a782e4b16fcbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/984768d670849c98c67ad8be723fcdf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
2 . 过抛物线
的焦点
作倾斜角为45°的直线
,直线
与抛物线
交于
,若
.
(1)抛物线
的方程;
(2)若经过
的直线交抛物线
于
,若
,求直线
的方程.
![](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/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82796f5bb05438453a1e06a4fa83d6a1.png)
(1)抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd1c7a08ce605d655b17c724730a077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439403928fdd014090c358649fdae49f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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名校
3 . 设点
为抛物线
的焦点,
,
,
三点在抛物线上,且四边形
为平行四边形,若对角线
(点
在第一象限),则对角线
所在的直线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290a56449ad6dd65aec7525c94273f59.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba6f4177822927b5875b92cd5f2038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b66c8377fa89deffc1ad5e96792a2b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2020-05-13更新
|
413次组卷
|
4卷引用:重庆市第八中学2020-2021学年高二上学期第二次月考数学试题
4 . 过点(0,4),斜率为-1的直线与拋物线y2=2px(p>0)交于两点A,B,如果OA⊥OB(O为原点),求拋物线的标准方程及焦点坐标.
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5 . 已知F为抛物线
焦点,A为抛物线C上的一动点,抛物线C在A处的切线交y轴于点B,以FA、FB为邻边作平行四边形FAMB.
(1)证明:点M在一条定直线上;
(2)记点M所在定直线为l,与y轴交于点N,MF与抛物线C交于P,Q两点,求
的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88eec86c17ca9025e2a6c7db421f5c37.png)
(1)证明:点M在一条定直线上;
(2)记点M所在定直线为l,与y轴交于点N,MF与抛物线C交于P,Q两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d6a2bfc85e28d4ed193011b58562d3.png)
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6 . 抛物线x2=-2y与过点P(0,-1)的直线l交于A,B两点,如果OA与OB的斜率之和为1,则直线l的方程是( )
A.Y=-x-1 | B.Y=x+1 | C.Y=x-1 | D.Y=-x+1 |
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