1 . 已知抛物线
的焦点为
,
是
上的一点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd1f7bf8f93c219c8716df185b66e1c.png)
__________ .
![](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/de4c8b859884022d8d2bd98b0500c116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd1f7bf8f93c219c8716df185b66e1c.png)
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2 . 如图,已知过抛物线
(
)的焦点
的直线与抛物线交于
两点,过点A作抛物线的准线的垂线
,垂足为
,抛物线的准线与
轴交于点
,
为坐标原点,记
,
,
分别为
,
,
的面积.若
,则直线
的斜率为______ .
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07ff78c166793f5e8d23f0b7f4be8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066afbd3603bccf7d9591c4ac48f552e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187e4941e2d8f5f8a1bb60f852588de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-04-22更新
|
855次组卷
|
4卷引用:河南省信阳市新县高级中学2024届高三4月适应性考试数学试题
河南省信阳市新县高级中学2024届高三4月适应性考试数学试题湖北省黄石市第二中学2023-2024学年高三下学期三模考试数学试题(已下线)四川省成都市外国语学校2024届高三高考模拟(五)理科数学试题辽宁省鞍山市第一中学2024届高三下学期八模数学试卷
3 . 已知抛物线
的焦点为F,过
作C的准线的垂线,垂足为M,FM 的中点为N,则直线PN的斜率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfb23a9e07213cb76990dbedfc7feca.png)
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解题方法
4 . 若点
在抛物线
上运动,点
在圆
上运动,
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4fb72e39d79b7a0cd892fa5fa34bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbfd8a1998196eeb7b465a5add0fa307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a56e5ddc6dc057aa4076130cc6ce19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5dadadb995eaeaeec45815c95259e7f.png)
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2024-04-12更新
|
435次组卷
|
2卷引用:河南省TOP二十名校2024届高三下学期4月冲刺一数学试卷
名校
5 . 已知
为抛物线
上两点,
为焦点,
为坐标原点,
在第一象限,且点
的纵坐标大于点
的纵坐标,若
,则点
的坐标为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f77a1f4739271a0adda2f9f7a46db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/30b06ca33d796b66023d51777eca3851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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解题方法
6 . 已知抛物线
的焦点
到其准线的距离为4,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
__________ ,
是
上一点,且点
,则
的最小值为__________ .
![](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/df5be1440d099f464ef46dee39de6010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354b980819c6ba892ce0e9ecead90634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b9e6530b912f758f9facbae31351c4.png)
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7 . 在平面直角坐标系中,若
的坐标
,
满足方程
,则点
的轨迹是__________ (填曲线的类型,填方程不给分).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5f443cc1db0eb6ad3975ddb1a9fc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
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2024-02-14更新
|
243次组卷
|
3卷引用:河南省济源市2023-2024学年高二上学期期末质量调研数学试题
河南省济源市2023-2024学年高二上学期期末质量调研数学试题(已下线)2.5 曲线与方程(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)上海市扬子中学2023-2024学年高一下学期期中考试数学试题
8 . 已知
是抛物线
上的一点,
为抛物线的焦点,
为坐标原点.当
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa3ba0c87ce97239cb65f863fa9340f.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.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/56bbafa889700c6764ebc7fc1a42cd91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dcf8baa7f4dff82b2c34db6e894f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa3ba0c87ce97239cb65f863fa9340f.png)
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2024-02-04更新
|
483次组卷
|
6卷引用:河南省郑州市宇华实验学校2023-2024学年高二下学期开学摸底考试数学试题
解题方法
9 . 抛物线
(
)上的动点Q到焦点的距离的最小值为2,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.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/df5be1440d099f464ef46dee39de6010.png)
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解题方法
10 . 已知F是抛物线
的焦点,M是C上一点,FM的延长线交y轴于点N,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf8eb88cfd81f78a3dc0e35f5c2f102.png)
___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fa758d23bfde6c1994505050fb65ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf8eb88cfd81f78a3dc0e35f5c2f102.png)
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