名校
解题方法
1 . 已知
为抛物线
的焦点,点
在
上,且满足
.
(1)求点
的坐标及
的方程;
(2)设过点
的直线
与
相交于
两点,且
不过点
,若直线
分别交
的准线于
两点,证明:以线段
为直径的圆恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](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/8823a20073c4dcdbc9c449f257a96447.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
您最近一年使用:0次
2024-02-23更新
|
238次组卷
|
2卷引用:湖南省株洲市第二中学2021-2022学年高二上学期第三次月考数学试卷
名校
2 . 如图,在正四棱柱
中,
,
,
、
分别为
和
的中点.
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.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/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1384ffba86ff08ce9e783d5d1bc51686.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bff3ccea5989c60e51e321af3f53f54.png)
您最近一年使用:0次
2024-01-27更新
|
220次组卷
|
5卷引用:湖南省株洲市第二中学2021-2022学年高二上学期第三次月考数学试卷
湖南省株洲市第二中学2021-2022学年高二上学期第三次月考数学试卷江苏省南通市2023-2024学年高二上学期期末数学考试江苏省睢宁高级中学2023-2024学年高二下学期3月学情检测数学试卷(已下线)模块一 专题6 《空间向量应用》(苏教版)(已下线)模块三 专题2 解答题分类练 专题3 空间向量线性运算(苏教版)
名校
解题方法
3 . 如图,四面体
中,
是正三角形,
是直角三角形,
,
.
(1)证明:平面
平面
.
(2)过
的平面交
于点
,若平面
把四面体
分成体积相等的两部分,求平面
与
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ecb138a844ef11bb3214cff0a475c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5fc4ad65b723b6a8da4c8dac154e6e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/5cde13af-b615-424c-a82d-99516a55edbd.png?resizew=167)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f332555e65843f32f4c623098c6adc72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383ec3453527947ed7a5960e9a8fbe0b.png)
您最近一年使用:0次
2023-10-12更新
|
157次组卷
|
2卷引用:安徽省安庆市第二中学2021-2022学年高二上学期10月阶段考试数学试题
名校
解题方法
4 . 已知抛物线
:
,坐标原点为
,焦点为
,直线
:
.
(1)若直线
与抛物线
只有一个公共点,求
的值;
(2)过点
作斜率为
的直线交抛物线
于
,
两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/6767830cc1811f0f4ea5a008fdc7e723.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2023-10-31更新
|
1765次组卷
|
18卷引用:2.4 抛物线(基础练)-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)
(已下线)2.4 抛物线(基础练)-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)甘肃省兰州市第一中学2021-2022学年高三上学期第一次月考(10月)数学(理)试题甘肃省兰州市第一中学2021-2022学年高三上学期第一次月考(10月)数学(文)试题陕西省部分名校2021-2022学年高三上学期10月月考文科数学试题陕西省部分名校2021-2022学年高三上学期10月月考理科数学试题(已下线)专题15 《圆锥曲线的方程》综合测试卷--《2021--2022高二上学期数学新教材配套提升训练(人教A版2019选择性必修第一册)》内蒙古自治区赤峰市林西县第一中学2021-2022学年高二上学期期中数学试文科题四川省内江市2022届高三零模数学理科试题四川省内江市2022届高三上学期零模数学文科试题(已下线)考点38 直线与圆锥曲线的位置关系-备战2022年高考数学一轮复习考点帮(浙江专用)(已下线)专题13 圆锥曲线-备战2022年高考数学(文)母题题源解密(全国乙卷)吉林省长春市第五中学2022-2023学年高二上学期期末数学试题(已下线)第七节 抛物线 第二课时 直线与抛物线的位置关系 A素养养成卷(已下线)考点14 直线与圆锥曲线相交问题 2024届高考数学考点总动员陕西省西安市阎良区关山中学2023-2024学年高二上学期期中数学试题山东省德州市禹城市第一中学2021-2022学年高二上学期期末模拟(五)数学试题(已下线)热点7-4 抛物线及其应用(6题型+满分技巧+限时检测)(已下线)专题25 抛物线的几何性质5种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)
名校
解题方法
5 . 抛物线
与直线
相交于
两个不同的点.
(1)当
时,求线段
的长;
(2)若
,求直线
的斜率
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd55f837e9c4e6bba1163ef13edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02f266bd253738e315e84231235f0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在三棱台ABC﹣A1B1C1中,∠BAC=90°,AB=AC=4,A1A=A1B1=2,侧棱A1A⊥平面ABC,点D是棱CC1的中点.
(1)证明:BB1⊥平面AB1C;
(2)求点B1到平面ABD的距离;
(3)求平面BCD与平面ABD的夹角的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/25/5fa0269a-4a15-451f-9d7b-85fe8c4d0087.png?resizew=165)
(1)证明:BB1⊥平面AB1C;
(2)求点B1到平面ABD的距离;
(3)求平面BCD与平面ABD的夹角的余弦值.
您最近一年使用:0次
2023-10-09更新
|
755次组卷
|
7卷引用:天津市静海区第一中学2021-2022学年高三上学期第二次阶段检测数学试题
名校
解题方法
7 . 在棱长为2的正方体
中,点
是
的中点,点
是
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/ed0bc78c-d5e1-4771-bdf3-a65aaaeda98f.png?resizew=160)
(1)试确定点
的位置,使得
平面
;
(2)若
是
的中点,求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/ed0bc78c-d5e1-4771-bdf3-a65aaaeda98f.png?resizew=160)
(1)试确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da81a007b14af667599765c89d5b8530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a76f52ae3ef071a5084d09ec035c80c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a76f52ae3ef071a5084d09ec035c80c.png)
您最近一年使用:0次
名校
8 . 如图,在四棱锥
中,
底面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8137ebd3ff7cbf25f71c270ceda9c390.png)
.
(1)求证:
平面
.
(2)若平面
与平面
的夹角的余弦值为
,求点A到平面
的距离.
![](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/8137ebd3ff7cbf25f71c270ceda9c390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/400b51a840a7b275ae90638962d9458b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/72d166ca-49ba-482a-9d73-9dcf1e95ff5b.png?resizew=129)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd3bd9c2db8c9f3cb8c6c7d7cbf5465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34cf4760da098099493d4627dacb878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2024-02-24更新
|
270次组卷
|
9卷引用:福建省宁化第一中学2021-2022学年高二上学期开学考试数学试题
福建省宁化第一中学2021-2022学年高二上学期开学考试数学试题河北省唐山市滦南县第一中学2021-2022学年高二上学期10月月考数学试题辽宁省新民市第一高级中学2021-2022学年高二上学期10月月考数学试题新疆乌苏市第一中学2022-2023学年高二上学期线上第二次月考数学试题河北省唐山市开滦第二中学2023-2024学年高二上学期10月月考数学试题安徽省安庆市怀宁县高河中学2023-2024学年高二上学期第三次月考数学试题广东省湛江市雷州市第二中学2023-2024学年高二下学期开学考试数学试题广东省深圳市深圳科学高中2023-2024学年高二下学期开学考试数学试题河南省焦作市第十一中学2023-2024学年高二上学期11月月考数学
名校
解题方法
9 . 如图,AB是圆柱的母线,BD是圆柱底面圆的直径,C是底面圆周上一点,E是AC上的点,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/c1ef8b8a-fcc8-4d80-8961-5ef567e1f5d7.png?resizew=121)
(1)求证:
;
(2)求直线BD与AC所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2ba31936561b06ec57a0ea893ada20.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/c1ef8b8a-fcc8-4d80-8961-5ef567e1f5d7.png?resizew=121)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a0d2a2415ec1e1374ac46bc232f450.png)
(2)求直线BD与AC所成角的大小.
您最近一年使用:0次
名校
10 . 如图,在正三棱柱
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/effd6aa0-ce25-4872-816b-6025d968c6f8.png?resizew=144)
(1)证明:
平面
;
(2)若
,求直线
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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/effd6aa0-ce25-4872-816b-6025d968c6f8.png?resizew=144)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1496afecd92a619fbe5e9b736f06f4e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeed487430a5b8a330f2d0c52166521a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
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