1 . 设
为平面上两点,定义
、已知点P为抛物线
上一动点,点
的最小值为2,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
_________ ;若斜率为
的直线l过点Q,点M是直线l上一动点,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093c6d5bcaa69cea79b24688f5d1bd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50061a63fdbd8394471c07f333d9fec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314837d3a10726c5f83528f791d20020.png)
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2024-06-04更新
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2 . 已知直线l:
分别与x轴,直线
交于点A,B,点P是线段AB的垂直平分线上的一点(P不在x轴负半轴上)且
.
(1)求点P的轨迹C的方程;
(2)设l与C交于E,F两点,点M在C上且满足
,延长MA交C于点N,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbb58ce273c92146fad009c73fce837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c811f42aeab9e84bf986baeb6beccc3.png)
(1)求点P的轨迹C的方程;
(2)设l与C交于E,F两点,点M在C上且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59af9b1d9c21276b422c27bd53ccd8a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4068a16181659ee65c778a4852a7492b.png)
您最近一年使用:0次
3 . 已知点
和点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9395c9b4769c1ae5fbfe5fd34771ac46.png)
之间的距离为2,抛物线
经过点N,过点M的直线l与抛物线C有两个不同的交点A,B,点E,F分别在直线
,
上,且
,
(O为坐标原点).
(1)求直线l的倾斜角的取值范围;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25e326fdf9e5456f48e8a99a069f379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9395c9b4769c1ae5fbfe5fd34771ac46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9237a77905f07b4b99fee49c7e2abb53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c023f4b501684abd869b36d6e6c7f21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1de080f965097aa7e1dd9e21fd8554a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9239ee786a3fe3aabd17ad5c61406.png)
(1)求直线l的倾斜角的取值范围;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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名校
解题方法
4 . 已知
,
是经过抛物线
焦点
的互相垂直的两条弦,若
的倾斜角为锐角,
,
两点在
轴上方,则下列结论中一定成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() |
B.设![]() ![]() ![]() |
C.若直线![]() ![]() ![]() |
D.![]() |
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解题方法
5 . 如图,已知抛物线
在点
处的切线
与椭圆
相交,过点
作
的垂线交抛物线
于另一点
,直线
(
为直角坐标原点)与
相交于点
,记
、
,且
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712433026957312/2714531731161088/STEM/b67f6c8f-4fc3-4a5b-9f8a-c09d4ce19dc0.png?resizew=203)
(1)求
的最小值;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4428756f1088ce78ed97cbcea99775f.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/9724fd240c60553bffc050d502e9a18a.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6270bb08b90f72d5671ab8225f356c43.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712433026957312/2714531731161088/STEM/b67f6c8f-4fc3-4a5b-9f8a-c09d4ce19dc0.png?resizew=203)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e86e6f0ac5903369afea2c8d04ba412.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fc44bdd2913504cd806ecbe56fc9fd.png)
您最近一年使用:0次
2021-05-05更新
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6卷引用:山东省日照市2023届高三下学期4月校际联合考试数学试题
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