1 . 已知动圆E过定点
,且y轴被圆E所截得的弦长恒为4.
(1)求圆心E的轨迹方程.
(2)过点P的直线l与E的轨迹交于A,B两点,
,证明:点P到直线AM,BM的距离相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
(1)求圆心E的轨迹方程.
(2)过点P的直线l与E的轨迹交于A,B两点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8547f2b4e89b0ae1445bda02d46f0668.png)
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解题方法
2 . 在四棱台
中,底面ABCD是正方形,且侧棱
垂直于底面ABCD,
,O,E分别是AC与
的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/17/2981496029151232/2982133741772800/STEM/dc198b51-e593-40c7-b014-2e7d2e2ddee1.png?resizew=187)
(1)求证:
平面
.
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8490b45704dd0002610e3e6e1de05b78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/2022/5/17/2981496029151232/2982133741772800/STEM/dc198b51-e593-40c7-b014-2e7d2e2ddee1.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af142a6050b54e8b5777a085d4597481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2095691cd6e3e50722061cbc0bb648.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e966a9f82e3caec6ee8698b3462fac6.png)
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4卷引用:青海省西宁市大通回族土族自治县2022届高三二模数学(文科)试题
青海省西宁市大通回族土族自治县2022届高三二模数学(文科)试题黑龙江省大庆市东风中学2021-2022学年高一下学期期末数学试题辽宁省实验中学2022-2023学年高二实验班上学期期初测试数学试题(已下线)8.5.2直线与平面平行(精练)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
名校
3 . 已知函数
,
.
(1)讨论
的单调性;
(2)任取两个正数
,当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a5cfe3859e67aedefd82ec9cb6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5179a1aa18466d91a92f81532a7b5b.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)任取两个正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3a5c22762b37be47859601bb1ebeec.png)
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9卷引用:青海省西宁市2023届高三一模理科数学试题
4 . 如图,在四棱柱
中,四边形ABCD是正方形,E,F,G分别是棱
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/2022/6/1/2991817753714688/2996335044198400/STEM/71f0f333-de44-4b84-b7cf-b3da87528b37.png?resizew=227)
(1)证明:平面
平面
;
(2)若点
在底面ABCD的投影是四边形ABCD的中心,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2022/6/1/2991817753714688/2996335044198400/STEM/71f0f333-de44-4b84-b7cf-b3da87528b37.png?resizew=227)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad4cbffc6d58be7ec916912b632ae58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4b75674b3bd22476b307419d4476b2.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b67f63997d21064d9c52494bd57d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7cfd72e190f8affc92d8d2a11068a6.png)
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5卷引用:青海省西宁北外附属新华联外国语高级中学2022-2023学年高三上学期期末考试数学(文)试题
青海省西宁北外附属新华联外国语高级中学2022-2023学年高三上学期期末考试数学(文)试题河南省部分学校2022届高三下学期5月考前最后一卷文科数学试题(已下线)专题22 空间中的平行关系(针对训练)-2023年高考数学一轮复习精讲精练宝典(新高考专用)(已下线)第03讲 空间直线、平面的平行 (精讲)-2(已下线)8.5.3 平面与平面平行 (精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
5 . 如图,在三棱柱
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/23/ca38b5ad-aef1-44a4-bebb-200dd08eb2ef.png?resizew=259)
(1)证明:平面
平面
.
(2)设P是棱
的中点,求AC与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bceb86f6a01109700263e97177c335eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29e8a1eefb6776168969a1155c9e9c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/23/ca38b5ad-aef1-44a4-bebb-200dd08eb2ef.png?resizew=259)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)设P是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d041feacf189306d130f4a949880bfc8.png)
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解题方法
6 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,证明:
.(注
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbc1e68e60a02d990d846b4303d551b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b717e559b68f93be0fa22d4275b09aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52881be613aa404e553da30d8987cfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dad09268b7cb8bfcbea010cb6d2a29e.png)
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3卷引用:青海省玉树州州直高中2021-2022学年高三下学期第四次大联考数学(理科)试题
名校
解题方法
7 . 已知定点
,定直线
,动圆
过点
,且与直线
相切.
(1)求动圆
的圆心轨迹
的方程;
(2)过焦点
的直线
与抛物线
交于
两点,与圆
交于
两点(
,
在
轴同侧),求证:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2347bec7975dab2b8bce2fd19b1237d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3a27c901fe58a919042c5d51126950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)求动圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffcaab0116abc15a0d30f2eee558833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880b3641052a3c5a82191f7d1e3ff338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6114947179bed8c2c86ac078e2f8497f.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a37a3c629b1d5d344a8226a8116a6b.png)
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2022-03-22更新
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5卷引用:青海省西宁市2022届高三二模数学(理)试题
解题方法
8 . 如图,在多面体ABCDEF中,四边形ABCD是正方形,AF
DE,
,DE⊥AD,AC⊥BE.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/35d1cf60-4498-429b-8114-9cc9a2b87b7d.png?resizew=146)
(1)证明:平面ADEF⊥平面ABCD.
(2)求平面ACE与平面ABF所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7003aee0b4b85f0fdd48ca9ae5826d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e5f4002264b874863fba6aae870464.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/35d1cf60-4498-429b-8114-9cc9a2b87b7d.png?resizew=146)
(1)证明:平面ADEF⊥平面ABCD.
(2)求平面ACE与平面ABF所成锐二面角的余弦值.
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7卷引用:青海省西宁市湟中区2022-2023学年高三上学期期中考试数学(理)试题
青海省西宁市湟中区2022-2023学年高三上学期期中考试数学(理)试题甘肃省靖远县第四中学2022-2023学年高三上学期第一次月考数学(理)试题重庆市2023届高三冲刺押题联考(二)数学试题(已下线)广东实验中学2024届高三上学期第一次阶段考试数学试题变式题15-18广东省揭阳市普宁市勤建学校2022-2023学年高二上学期第一次调研数学试题福建省南安市柳城中学2022-2023学年高二上学期11月期中考试数学试题(已下线)期中真题必刷常考60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
解题方法
9 . 已知函数
,曲线
在
处的切线与直线
垂直.
(1)求
的值.
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d95aa7445ae32ebce0f7aa3a284327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f129d441ab39d195cb2580c46065d0fb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac0c4f74d16d30a8799b03b41460cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c62b3c44e262862c5d29c0d28ae17c6.png)
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2卷引用:青海省西宁市大通回族土族自治县2022届高三第二次模拟考试数学(理科)试题
10 . 已知
是椭圆
的右焦点,
,原点O到直线MF的距离为
,点
在E上.
(1)求E的方程.
(2)过点F作直线与E交于A,B两点,直线MA,MB与y轴分别交于H,G两点,证明:H,G关于点
对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24550b13dbecf7d86c7054250e987274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e106f614e2e66bc05d7e38ea6042a370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe8530b8e246a9a5ec9fe3b9c347d5a.png)
(1)求E的方程.
(2)过点F作直线与E交于A,B两点,直线MA,MB与y轴分别交于H,G两点,证明:H,G关于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef66a0582e95fb5c57a405acdea9a.png)
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2022-05-18更新
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