名校
解题方法
1 . 已知正方体
的棱长为1,空间中一动点
满足
,
分别为
的中点,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b963c0c29bcb13c2dc93ae9abf53a841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a5f302c1c2f7e1b46cad05594ed672e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92178a5c6a76586292f622da298a8db.png)
A.存在点![]() ![]() ![]() |
B.设![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.三棱锥![]() ![]() |
您最近一年使用:0次
2024-06-08更新
|
325次组卷
|
2卷引用:重庆市西南大学附属中学2024届高考全真模拟数学试题
解题方法
2 . 已知棱长为1的正方体
内有一个动点M,满足
,且
,则四棱锥
体积的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8c425e2bc51c94717ee613f9a6dff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440e8409121aff14ec2d2d7f3919a150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0db0dfbebfda04286949b1f11efb36.png)
您最近一年使用:0次
3 . 已知
,曲线
上任意一点到点
的距离是到直线
的距离的两倍.
(1)求曲线
的方程;
(2)已知曲线
的左顶点为
,直线
过点
且与曲线
在第一、四象限分别交于
,
两点,直线
、
分别与直线
交于
,
两点,
为
的中点.
(i)证明:
;
(ii)记
,
,
的面积分别为
,
,
,则
是否为定值?若是,求出这个定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5660be1b6e0d3d1cab756d6f8f5855.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/b650820d7bed48ed67a2869ad8c65ff1.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知曲线
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b85d79eabe4ce65b09f16a202c6b017.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba08ef7e19164e78dc0dc08fe4395d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135361ee2e038ca0dd890b701ac1ef5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740eea87967a331d7da821592a639076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc80d8bbc5fec873686719e78bd518d.png)
您最近一年使用:0次
解题方法
4 . 已知点为圆
上任意一点,
,线段
的垂直平分线交直线
于点
.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e178e28fb14e7f6a7e09d3ed7bcbe89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
5 . 在平面直角坐标系
中,已知点
、
,
的内切圆与直线
相切于点
,记点M的轨迹为C.
(1)求C的方程;
(2)设点T在直线
上,过T的两条直线分别交C于A、B两点和P,Q两点,连接
.若直线
的斜率与直线
的斜率之和为0,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ebf8646ffd394fde760dbd7e0ce30b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e2d5f57373207c650951eaa25fc289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adb619ca92790d5d3fa7652210ff8eb.png)
(1)求C的方程;
(2)设点T在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0d7b3be178c12f10c2c7b9fb410c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4773daf2e8490b26f0d0c976a6cefc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4313014eee5bc5064d07d4a33f9973c8.png)
您最近一年使用:0次
2023-07-15更新
|
1267次组卷
|
4卷引用:重庆市巴南区2024届高三诊断(一)数学试题
重庆市巴南区2024届高三诊断(一)数学试题河南省驻马店市2022-2023学年高二下学期期末数学试题(已下线)重难点突破09 一类与斜率和、差、商、积问题的探究(四大题型)(已下线)专题3-4 双曲线大题综合10种题型归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)
6 . 在棱长为4的正方体中,点E为棱
的中点,点F是正方形
内一动点(含边界),则下列说法中正确的是( )
A.直线![]() ![]() ![]() |
B.平面![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2023高三·全国·专题练习
解题方法
7 . 已知在三棱锥
中,
,
,平面PAC⊥平面ABC.若点M为BC的中点,点N为三棱锥
表面上一动点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239b038c44b3d1b3c80084b5a2aa6fb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1f4f255d191786f7d330d278868c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
A.三棱锥![]() ![]() | B.直线PC与AM所成的角![]() |
C.若![]() ![]() | D.若点N在棱AC上,则![]() |
您最近一年使用:0次
解题方法
8 . 已知椭圆
:
的长轴长是短轴长的2倍,直线
被椭圆截得的弦长为4.
(1)求椭圆
的方程;
(2)设M,N,P,Q为椭圆
上的动点,且四边形MNPQ为菱形,原点О在直线MN上的垂足为点H,求H的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d585d2d6643471640905d234d9538c5.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设M,N,P,Q为椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
9 . 已知点
,动点
到直线
的距离为
,且
,记
的轨迹为曲线
.
(1)求
的方程;
(2)过
作圆
的两条切线
、
(其中
、
为切点),直线
、
分别交
的另一点为
、
.从下面①和②两个结论中任选其一进行证明.
①
为定值;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d314b47d37c9f58e05ad11f3e68e27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b114dd62d9fe5538a5e7335c3c5642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec92f17bd6b9ba94a39eea144b9dd9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83652fb25335782f86018ff3ebfb23cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.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/7f9e8449aad35c5d840a3395ea86df6d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a1383c7a8c8b49d7704ca6d6b37107.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60097cec26b613837579cff70a863a42.png)
您最近一年使用:0次
10 . 已知棱长为3的正四面体
,
是空间内的任一动点,且满足
,E为AD中点,过点D的平面
平面BCE,则平面
截动点P的轨迹所形成的图形的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857edd51a710495c0c8a96e3760e4404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31e45e4cb398f3c74aed277d6b72515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.π | B.2π | C.3π | D.4π |
您最近一年使用:0次
2022-03-15更新
|
1100次组卷
|
6卷引用:重庆市缙云教育联盟2022届高三下学期3月质量检测数学试题
重庆市缙云教育联盟2022届高三下学期3月质量检测数学试题浙江省“超级全能生”22021-2022学年高考选考科目3月联考数学试题(已下线)2022年新高考北京数学高考真题变式题9-12题(已下线)第五篇 向量与几何 专题18 空间点线面问题 微点2 空间点线面问题综合训练(已下线)专题14 立体几何常见压轴小题全归纳(练习)(已下线)第三章 空间轨迹问题 专题四 立体几何轨迹面积、体积问题 微点2 立体几何轨迹面积、体积问题综合训练【培优版】