2024·全国·模拟预测
解题方法
1 . 如图,在平面直角坐标系
中,
为矩形
的边
的中点,且
,
为
的中点.对于任意的
,将线段
和
分成
等分,设
上的分点为
和
,过
上的分点
作与
平行的直线
,
与直线
交于点
,利用对称性作出
关于
对称的另一半的点,用光滑曲线把它们连接起来,得到曲线
(过坐标原点
).设
,
为曲线
上的一个动点,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4d576e1696658c1e959b41ccf85739.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cd68cc82e90a5e2049a7ea3171b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04f3f1e2307ddb2e5111b36ab9e908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fa7c897541e8a7c75d9529061bc138.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/10/9ead9151-75e3-43ff-b32f-6b7b69e2d30a.png?resizew=195)
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2 . 设点
在抛物线
上,已知
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
__________ ;若
,则直线
斜率的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ac6188f40414f76bc754dee4a75809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e48b0ba6fbb831b99e0868a3c91cafa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a79a4c82b46d2032adfb0659c7434cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee21db6628e4db3f5831370549fa96b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
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2024-04-03更新
|
576次组卷
|
2卷引用:北京市北师大附属实验中学2024届高三下学期3月零模数学试题
解题方法
3 . P为抛物线上任意一点,点
,设点P到y轴的距离为d,则
的最小值为
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2024-03-31更新
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366次组卷
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2卷引用:陕西省咸阳市2024届高三下学期高考模拟检测(二)数学(文科)试题
4 . 已知抛物线
的焦点为
,点
在
上,若
,则
到直线
的距离为:________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32d1cbd3ee6d1a210a8eae153ac5bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/7763fe9b98015f0022975a759756d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
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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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6 . 已知抛物线
上的点P到抛物线的焦点F的距离为6,则以线段PF的中点为圆心,
为直径的圆被x轴截得的弦长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac654a052f98d1ccb7fede1f122cec3.png)
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2024-03-25更新
|
843次组卷
|
2卷引用:天津市河西区2024届高三下学期第一次质量调查数学试题
名校
7 . 已知抛物线
的焦点为
,点
为抛物线上一点,以
为圆心的圆经过原点
,且与抛物线的准线相切,则该抛物线的焦点到其准线的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db5b13f5ad91e8ecd233623bb5f5016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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2024-03-25更新
|
230次组卷
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2卷引用:广东省广州市铁一中学2023-2024学年高二下学期3月月考数学试题
名校
解题方法
8 . 抛物线
的焦点F,点A,B在抛物线上,且
,弦AB的中点M在准线上的射影为N,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b98e91240001ff3210f3b9fc67adb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b5a34215542bec52ba524bd6e304ac.png)
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2024-03-25更新
|
652次组卷
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3卷引用:重庆市第十一中学校教育集团2024届高三第七次质量检测(3月)数学试题
解题方法
9 . 已知抛物线
的焦点为
,
是
上的动点,过点
作直线
的垂线,垂足为
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fdedd1db38755989cd462c151f5106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0869b06153ae7492b623677c1f30b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d968044241d03105c05c40fd6b94264.png)
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解题方法
10 . 设
为抛物线
的焦点,直线
,点
为
上任意一点,过点
作
于
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53b3368052f5eb9c0d27a1d3dc249ec.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b871eae04a8d29a655fdf9a23f77e58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4180dae966f648d368a10edf3b7e3c3.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/904b21bba351171abdc8482a906499d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53b3368052f5eb9c0d27a1d3dc249ec.png)
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