1 . 已知抛物线C的标准方程为
,O为坐标原点,直线l为其准线,点A,B是C上的两个动点(不是原点O),线段
与x轴交于点M,连接
并延长交准线于点D,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
A.若点M为C的焦点,则直线![]() |
B.若点M为C的焦点,则线段![]() |
C.若![]() |
D.若![]() ![]() |
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2 . 抛物线有如下光学性质: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.已知抛物线
,
为坐标原点,一束平行于
轴的光线
从点
射入,经过
上的点
反射后,再经
上另一点
反射后,沿直线
射出,且
经过点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388c361a4f70897c7b02c3885e48f178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.当![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() ![]() |
C.![]() |
D.设该抛物线的准线与![]() ![]() ![]() |
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2卷引用:重庆市三峡名校联盟2023-2024学年高二上学期联考数学试卷
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3 . 过抛物线
的焦点为F的直线l与C相交于
两点,若
的最小值为6,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7d5b7a335fb30a034976287aee9e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac35b1e8a952aac4f4cdaaf02d868d04.png)
A.抛物线的方程为![]() | B.MN的中点到准线的距离的最小值为4 |
C.![]() | D.当直线MN的倾斜角为![]() ![]() |
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4 . 已知抛物线
,过其焦点
的直线
与抛物线
交于P,Q两点(点P在第一象限),
,则直线
的斜率为______ 若
,点
为抛物线
上的动点,且点
在直线
的左上方,则
面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3520a32741ec83b37a30d68b30c759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f05fc6915220cf15717ff47b31c33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
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3卷引用:重庆市綦江南州中学校2022-2023学年高二上学期期末数学试题
5 . 若抛物线C:
,且A、B两点在抛物线上,F为焦点,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
A.若A、B、F共线,则![]() |
B.若![]() ![]() |
C.经过点![]() |
D.若![]() |
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6 . 设抛物线
的焦点为
,准线为
,过焦点的直线交抛物线于
,
两点,分别过
,
作
的垂线,垂足为
,
,若
,则三角形
的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce50eb3d71e81613c4dac1e8ecae6db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
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7 . 已知抛物线
的焦点为
,准线为
,过
的直线与
交于
,
两点,分别过
,
作
的垂线,垂足为
,
,
,
,
为
中点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce50eb3d71e81613c4dac1e8ecae6db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7f2be120cab23463d194941d51fe34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.直线![]() ![]() | B.![]() |
C.![]() | D.![]() ![]() ![]() |
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2014·吉林长春·三模
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8 . 已知抛物线C:y2=2px(p>0)的焦点为F,若过点F且斜率为1的直线与抛物线相交于M,N两点,且|MN|=8.
(1)求抛物线C的方程;
(2)设直线l为抛物线C的切线,且l∥MN,P为l上一点,求
的最小值.
(1)求抛物线C的方程;
(2)设直线l为抛物线C的切线,且l∥MN,P为l上一点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f4ea7498731e5af223a75a5ab7f32c.png)
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2019-08-16更新
|
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9 . 设点
,动圆P经过点F且和直线
相切,记动圆的圆心P的轨迹为曲线C.
(1)求曲线C的方程;
(2)点
,过F的直线交C于
两点,连接
,与C的另一个交点分别为
,记直线
的斜率分别为
.求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce88a93d98e20ef97c0b8bb67af3502b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1c84057882768f20a01365c81b6760.png)
(1)求曲线C的方程;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/470d39b666e5101a7e6349274d04f172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3decff252399c7e952cfe5ead2294dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e6734f82473aa9fd35c208d11ee4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
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10 . 已知
,
是过抛物线
(
)焦点
的直线与抛物线的交点,
是坐标原点,且满足
,
,则抛物线的标准方程为
![](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/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a1e54e71535567058a95e1351ffa79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f32f04a22b5be93b4009f635b900dc4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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