1 . 已知曲线
,试证明:对
的任意直径
,均存在
上的动点P,使得
均与
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ffaa45c5bdef21966bd436f515be14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
名校
解题方法
2 . 对抛物线
,定义:点
叫做该抛物线的焦点,直线
叫做该抛物线的准线,且该抛物线上任意一点到焦点的距离与它到准线的距离相等.运用上述材料解决以下问题:
如图,已知抛物线
:
的图象与
轴交于
、
两点,且过点
.
(1)求抛物线
的解析式和点A坐标;
(2)若将抛物线C的图象向左平移4个单位,再向上平移4个单位得到抛物线D的图象.
①设
为抛物线
上任意一点,
轴于点N,求
的最小值;
②直线l过抛物线D的焦点且与抛物线D交于
两点,证明:以
为直径的圆与抛物线D的准线相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa0e961df94bc4cc1c8407ed65f2557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd81b3c7a12b2c2623d4336751e3ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423f5e7781b94f96ff4aac23cba2964d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/7/ab0eb186-9b21-435c-8f0d-4c645bfd9955.png?resizew=343)
如图,已知抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6c4cd33c7a1f5d3b5ea44a3e03610c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/be4715dd5f2139c84d0302095d226302.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若将抛物线C的图象向左平移4个单位,再向上平移4个单位得到抛物线D的图象.
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52cbeb9b1c1d637b903cf3e5c7f730f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed953fccffc4f4d133e7a41472127d7.png)
②直线l过抛物线D的焦点且与抛物线D交于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
解题方法
3 . 如图①,
是梯形
的高,
,现将梯形
沿
折起成如图②的四棱锥
,使得
.点E是线段
上一动点.
![](https://img.xkw.com/dksih/QBM/2023/4/6/3210683025580032/3210718068342784/STEM/25a581f915434858ab85dbca14e4bc5b.png?resizew=463)
(1)判断
和
是否可能垂直,并说明理由.
(2)当
时,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd06501e333d6501c171640ccf05414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b744576b325f894cc71ffa1aa4d38b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9641d01140939c44450bf39773272af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2023/4/6/3210683025580032/3210718068342784/STEM/25a581f915434858ab85dbca14e4bc5b.png?resizew=463)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b17ba2410af31808093fc780fd2438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
解题方法
4 . 已知空间有A,B,C,D四个点,满足
,空间中还有
四点,满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50980a3c7c299a994c9369e6c8403826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57771773279c108bc8e1af3d64c94318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f7a7462f455eae1b2d83456f529642.png)
您最近一年使用:0次
解题方法
5 . 如图,开口向右的抛物线对称轴与x轴重合,焦点位于坐标原点处,并且过点
.设直线
与抛物线交于
两点,直线
看与抛物线交于
两点.
![](https://img.xkw.com/dksih/QBM/2023/2/7/3169711929909248/3169843440074752/STEM/cdb8ea8fb97149f8848f61456cc00bd0.png?resizew=317)
(1)求抛物线方程.
(2)求证:
.
(3)设直线
分别与y轴交于P,Q两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc756fb11c7c96bf318b5fae4982f507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47aca422a33ec9b9430d204659ff9fbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c345dfe2ac9387357be143c0b96de6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756f66428eba953d4610f59a3479d143.png)
![](https://img.xkw.com/dksih/QBM/2023/2/7/3169711929909248/3169843440074752/STEM/cdb8ea8fb97149f8848f61456cc00bd0.png?resizew=317)
(1)求抛物线方程.
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d298273d6dc5a07cc6f819ac3e63730.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15abfafc59b6f9f01f3be4db4df797d.png)
您最近一年使用:0次
6 . 已知椭圆
的焦点坐标为
,若直线l与椭圆
相切,点
到直线l的距离分别为
.证明:
(1)
.
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe6c4c8fffd4c5b21f1d11b26963fcf.png)
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c118b51ab426bc1c1b56179094f146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475a3fdc7b27d5ffa8c864dc478903d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2f1c1409a06278e847e6b573cef254.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fc0e502b29162d63e46d46220cce8e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe6c4c8fffd4c5b21f1d11b26963fcf.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8acbfb924b9d207b057fc6593ffeb9d9.png)
您最近一年使用:0次
7 . 已知函数
在定义域
上严格单调递增.
(1)证明:函数
至多存在一个零点.
(2)若函数
存在零点
,证明:存在
,使得
对于任意
恒成立的充分必要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a19bbab2270fc8e694527e801556cf.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07cbf6c4e062852a2bdee01b9992713b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad65ff0ab0a64844ab78062df2e6ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13747fa9a42164caebe2c9b7c5d06d3a.png)
您最近一年使用:0次
解题方法
8 . 如图,已知抛物线
,点A在抛物线上,且在第一象限,以点A为切点作抛物线的切线l交x轴于点B,过点B作垂直于l的直线
交抛物线于C,D两点,其中点C在第一象限,设
与y轴交于点K.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/34e3d803-c747-4660-a65a-42f14b74a55c.png?resizew=248)
(1)若点A的横坐标为2,求切线l的方程.
(2)连结
,记
的面积分别为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/34e3d803-c747-4660-a65a-42f14b74a55c.png?resizew=248)
(1)若点A的横坐标为2,求切线l的方程.
(2)连结
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1bf0ea1c9191c3c88acf28bff2c4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c68e39785ea98cde06005ff449b3a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958608935f2e6d69c15cb1f130428245.png)
您最近一年使用:0次
名校
解题方法
9 . 在三棱台
中,
,
,
,
,且
平面
.设P、Q、R分别为棱AC、FC、BC的中点.
![](https://img.xkw.com/dksih/QBM/2021/5/10/2718156869746688/2764564908343296/STEM/38b8d99319df42c8ae945ef1122725a9.png?resizew=173)
(1)证明:平面
平面PQR;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69080f189163f21f1c63e7a74c7a7d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bc4c9dd737193f7acce692b23500d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2021/5/10/2718156869746688/2764564908343296/STEM/38b8d99319df42c8ae945ef1122725a9.png?resizew=173)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309e58bf083bad13abd549720a63a22.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d682fd0344452998187cb6d48de3dd1.png)
您最近一年使用:0次
2021-07-15更新
|
414次组卷
|
3卷引用:湖南师范大学附属中学2020-2021学年高二下学期期中数学试题
湖南师范大学附属中学2020-2021学年高二下学期期中数学试题(已下线)期中重难点突破专题01-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)2021年清华大学语言类保送暨高水平艺术团数学试题