1 . 已知多边形
是边长为2的正六边形,沿对角线
将平面
折起,使得
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253824942080/2716180000137216/STEM/0bf43215-fcf8-4c37-89ab-4a645ed7d047.png?resizew=402)
(1)证明:平面
平面
;
(2)在线段
上是否存在一点
,使二面角
的余弦值为
,若存在,请求出
的长度;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983a8d7745d1440cdbc7e6a65b25c3c6.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253824942080/2716180000137216/STEM/0bf43215-fcf8-4c37-89ab-4a645ed7d047.png?resizew=402)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26955cc70b37276a25e50d70a587744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
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解题方法
2 . 如图,
是棱长为1的正方体.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253610491904/2716459014283264/STEM/2ba922eb-cbfe-4ad5-8d72-87a494325831.png?resizew=284)
(1)求证:平面
平面
;
(2)在棱
上是否存在点
,使得二面角
的平面角与二面角
的平面角相等,如果存在,求出
的长,如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253610491904/2716459014283264/STEM/2ba922eb-cbfe-4ad5-8d72-87a494325831.png?resizew=284)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d9cb67314af122defeaa715365a9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7ba7cd0c654714c967a900513ba16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
3 . 已知圆
:
,点
,P是圆C上任意一点,线段AP的垂直平分线交CP于点Q.
(1)求点Q的轨迹方程;
(2)过点
作直线MN交点Q的轨迹于M、N两点,设线段MN的中点为H,判断线段
与
的大小,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afc954e87bd737ec051d5c94837c8a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
(1)求点Q的轨迹方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3544997cc034ed882c0d0a3bdbf5f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa8299316c747f7e8c54ee2b073a17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4713d7ccecd5cdcb3efad32eb39338c4.png)
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解题方法
4 . 已知椭圆
的短轴的两个端点分别为
,
,焦距为
.
(1)求椭圆
的方程;
(2)已知直线
与椭圆
有两个不同的交点
,
,设
为直线
上一点,且直线
,
的斜率之积为
,证明:点
在
轴上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3544997cc034ed882c0d0a3bdbf5f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
5 . 已知直线
与圆
相切,动点
到
与
两点距离之和等于
,
两点到直线
的距离之和.
![](https://img.xkw.com/dksih/QBM/2021/2/24/2664907416420352/2666441856196608/STEM/53b9b5f9-7d6f-4bc1-9e32-2cf9cf308f6a.png?resizew=263)
(1)设动点
的轨迹为
,求轨迹
的方程;
(2)对于椭圆
,上一点
,以
为切点的切线方程为
.设
为
上任意一点,过点
作轨迹
的两条切线
,
,
,
为切点.
①求证直线
过定点;
②求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393a0e30b023f2a20d366eef481b5eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851ef4a896431db824adb1b9af3dd1e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c2124260496e9307d6448c0c943f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2021/2/24/2664907416420352/2666441856196608/STEM/53b9b5f9-7d6f-4bc1-9e32-2cf9cf308f6a.png?resizew=263)
(1)设动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)对于椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb57bb18755127be041d346444a4743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46c2737bf9c790cdb4b767217719452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9e953a4a5f98c96bbe67cbaadf76d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a459f78e4a3516d8a8535290ede7f386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
①求证直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ea1c3fe8431260ecb8dffcdae8d570.png)
您最近一年使用:0次
2021-02-26更新
|
1166次组卷
|
3卷引用:新疆维吾尔自治区2021届高三第二次联考数学(理)能力测试试题
新疆维吾尔自治区2021届高三第二次联考数学(理)能力测试试题(已下线)专题1.11 圆锥曲线-定点、定值、定直线问题-2021年高考数学解答题挑战满分专项训练(新高考地区专用)四川省成都市玉林中学2023-2024学年高二上学期期末模拟数学试题(二)
名校
6 . 如图,在直三棱柱
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/5/11/2718965993095168/2720429408911360/STEM/ec9cee32-eb32-4f0b-a9d9-de5b18147040.png?resizew=304)
(1)若
为
上的一点,且
,求证
;
(2)在(1)的条件下,若异面直线
与
所成的角为
,求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef71ad329f7c4e0e8d409f279787e2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2021/5/11/2718965993095168/2720429408911360/STEM/ec9cee32-eb32-4f0b-a9d9-de5b18147040.png?resizew=304)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca861956f4410fae22f6d49dd1b7c098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb56ba18161d012a69aee3743b8a0f9.png)
(2)在(1)的条件下,若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
您最近一年使用:0次
2021-05-13更新
|
435次组卷
|
3卷引用:新疆维吾尔自治区布尔津县高级中学2021届高三三模数学(理)试题
新疆维吾尔自治区布尔津县高级中学2021届高三三模数学(理)试题(已下线)一轮复习大题专练50—立体几何(线面角2)—2022届高三数学一轮复习广东省深圳市龙城高级中学2022届高三上学期9月第一次月考数学试题
7 . 已知点A,B分别为椭圆
的左、右顶点,过左焦点
的直线l与椭圆C交于P、Q两点,当直线l与x轴垂直时,
.
(1)求椭圆的标准方程;
(2)设直线
,
的斜率分别为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d725494ad76dc0ef160cf05af0f1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e69e6905087dcd9fc28c777242dc49.png)
(1)求椭圆的标准方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
您最近一年使用:0次
解题方法
8 . 如图,在三棱锥
中,平面
平面
是等边三角形,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/a03837f5-597f-4633-865b-13e1fe57a0df.png?resizew=145)
(1)求证
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eafd509d9cc5c7618aee2967105364b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc060366fff50795ac657153653117e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7490886e2807c7b8a4fa57d99c4dc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d25599d59d4b2f54f8537108fdcc41.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/a03837f5-597f-4633-865b-13e1fe57a0df.png?resizew=145)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7e56367ffbcd363e8734d9314750b5.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2edd3e5b926b9bb6e34ef4ada50914.png)
您最近一年使用:0次
名校
解题方法
9 . 如图所示,四棱锥
中,
菱形
所在的平面,
,点
、
分别是
、
的中点,
是线段
上的点.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712254176993280/2716164909015040/STEM/67199f5f-1d6a-40af-a84b-c0c36bb60e1b.png)
(1)求证:平面
平面
;
(2)当
时,是否存在点
,使直线
与平面
所成角的正弦值为
?若存在,请求出
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712254176993280/2716164909015040/STEM/67199f5f-1d6a-40af-a84b-c0c36bb60e1b.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4584c65793fca5b4c0d847275ca5c766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a109c829d652632a88ade6924fcda206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47548785e478bc5b9591341a881e3127.png)
您最近一年使用:0次
2021-05-07更新
|
939次组卷
|
5卷引用:新疆维吾尔自治区2021届高三年级第二次诊断性测试数学(理)试题(问卷)
名校
解题方法
10 . 如图,在直四棱柱
中,底面
为矩形,
,
在棱
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/395b7a45-708f-495b-b926-e138e47bda9e.png?resizew=158)
(1)若
为
的中点,求证:平面
平面
;
(2)若二面角
的余弦值为
时,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5123bb63aa67fe23f5dd3e19fa4b4571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/395b7a45-708f-495b-b926-e138e47bda9e.png?resizew=158)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addc18d788c8ea6a6b6bb01515b620a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2608c0af8b1da70e2d67e404ffe75e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
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2021-01-09更新
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114次组卷
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2卷引用:新疆2021届高三年级第一次联考数学(理)试题