1 . 如图,已知
内接于抛物线
,且边
所在直线分别与抛物线
相切,F为抛物线M的焦点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/9363e490-d4f9-4149-82da-1203d0f10886.png?resizew=200)
(1)边
所在直线与抛物线M相切;
(2)A,C,B,F四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854f480c60b88b546cb15d3b5622e212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12bc980a6ff5fe01b746c65af072a05e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19409d6d120387b3bccd934c4911bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd646f98b097a1b09f0b8a76ec399340.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/9363e490-d4f9-4149-82da-1203d0f10886.png?resizew=200)
(1)边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)A,C,B,F四点共圆.
您最近一年使用:0次
2 . 甲乙二人轮流给一个正方体的棱涂色,首先,甲任选3条棱涂成红色,然后乙从余下的9条棱中任选3条涂成绿色,接着甲从余下的6条棱中任选3条涂成红色,最后乙将余下的3条棱涂成绿色,如果甲能将某个面上的4条边全都涂成红,甲就获胜,试问甲有必胜策略吗?说明理由.
您最近一年使用:0次
3 . 求所有正整数n和素数p满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0643ae72df91edd0a73c3b986e6e60e9.png)
您最近一年使用:0次
4 . 函数
的图像酷似教师批改作业时所画的“对勾”,所以我们常称
为“对勾函数”.其图像是双曲线,其渐近线方程为
(即
轴)与
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/c28cc4cf-c4ed-40e7-9c26-b0a8365caa55.png?resizew=165)
(1)求C顶点的坐标与离心率;
(2)求C焦点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16803c866fdda79e4a0ebaef33b48f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14fd2128777226fdda969aaaa541cea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcf9bfbf771cb6118f8e631724314e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fdb3bf31cb105ddfe045d24f929ce6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/c28cc4cf-c4ed-40e7-9c26-b0a8365caa55.png?resizew=165)
(1)求C顶点的坐标与离心率;
(2)求C焦点坐标.
您最近一年使用:0次
5 . 已知半径为1的圆上有2022个点,求证:至少存在一个凸337边形,它的面积小于
.(
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd083f64769b1e6e111cbb2c7a607b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e87caa2c8b8ba691f9cd2a9570be6ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe92d84d3b33b8675bd1ae6e61967ba0.png)
您最近一年使用:0次
6 . 已知
是曲线
上的点,C在
处的切线
交
轴于点
,过
作
轴的垂线交C于
,C在
处的切线
交
轴于
,过
作
轴的垂线交C于点
,C在
处的切线
交
轴于
,过
作
轴的垂线交C于
,重复上述操作,依次得到
,
,……,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b088cb297522e38dff96a4b5ea600e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a098a0e65cc3a678c09ba4b90b97d91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e367975cd9882f21334ffc8a92745161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9051c36cd615f33b0b998d098e49f0ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0235feb6050c98ad45cca7ceceaaf431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f1b40221f57567c67c1ba5ceb2f57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f1b40221f57567c67c1ba5ceb2f57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c57033e396170c7546b3f76e0cb5f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d9d82c1949784452addc8047894384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ec9341909c0edd74ee755543c4c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ec9341909c0edd74ee755543c4c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92adfef6c3f4b8c041958fbf0b01f6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0269c74f81a17eca13334d53a3ae6176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82cfd620516c5812e213ed4e0534a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e056ec49e2b47361345a4db01ce788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c643b0ffd4ca67a657e04a1337faac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d94f45a4cdb64e26f49c2490aaccd8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297b6b3b19cde9602ca48acf1030e7d1.png)
您最近一年使用:0次
7 . 如图,“爱心”是由曲线
和
所围成的封闭图形,在区域
内任取一点A,则A取自“爱心”内的概率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454a4be11ab1e6ab54f393c0b48cb6a6.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea66cea52830fb855282de4266399cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ace4d72fbb3de77e5611f427583302b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd7dac2b4af73fa517daa230c03b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454a4be11ab1e6ab54f393c0b48cb6a6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/35896cc8-9c79-4686-ac95-4bc233a562da.png?resizew=158)
您最近一年使用:0次
8 . 甲烷分子
的四个氢原子位于棱长为1的正四面体的四个顶点,碳原子C位于四面体的中心
,记四个氢原子分别为
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13d906ff99fdc08d57f4de3785580c0.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33fbdd535c70284a4e988fff972e4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e6fecc49564bf3341dc355e0ec4d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dd27548b6259e9e7dced1a7e22cb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0c83fcca59db51cff4e3995c45081e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54253784d559487fe67009c9223cb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9f017376a9c9c31829722d27857012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13d906ff99fdc08d57f4de3785580c0.png)
您最近一年使用:0次
9 .
,使得
(
)恒成立,则所有满足条件的a的和_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77ab2f1b0816ae06cb935345f624492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e759103cd9b8d37953372a77069087f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7b12c67764d968add8f397e2655385.png)
您最近一年使用:0次
10 . 如图,M,N分别是
两直角边上的动点,P是线段MN的中点,则以下结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/7b7d00f8-8d9f-46a1-96b9-879a897c94bc.png?resizew=118)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/7b7d00f8-8d9f-46a1-96b9-879a897c94bc.png?resizew=118)
A.当△AMN的面积为定值时,点P的轨迹为双曲线一支 |
B.当|MN|为定值时,点P的轨迹为一圆弧 |
C.当![]() |
D.当△AMN的周长为定值时,点P的轨迹为抛物线 |
您最近一年使用:0次