1 . 在三棱锥
中,M是平面ABC上一点,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abceecd4d1784633c5e1faf0bfe0dd32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
A.1 | B.![]() | C.![]() | D.![]() |
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5卷引用:山西省运城市2022-2023学年高二上学期期末数学试题
山西省运城市2022-2023学年高二上学期期末数学试题山西省吕梁市2022-2023学年高二上学期期末数学试题(已下线)第01讲:空间向量(必刷9大考题+9大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019选择性必修第一册)(已下线)2.3.1 空间向量的分解与坐标表示(同步练习)-【素养提升—课时练】2022-2023学年高二数学湘教版选择性必修第二册检测(基础篇)(已下线)第06讲 空间向量及其线性运算4种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)
解题方法
2 . 已知F是抛物线
的焦点,点
,抛物线上两点A,B满足
,则
与
(其中O为坐标原点)面积之和的最小值是________ ,此时
的值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1086c0c42a65a0ec55d1cb03d6b5e88d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242dc4cf2720b503e26ec8017d31444f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ccb7249e93a9c9e85021436eeb039e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa0505b8c375d6bdbc66d16e10c527e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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3卷引用:山西省运城市2022-2023学年高二上学期期末数学试题
3 . 已知椭圆
的左右焦点分别为
,椭圆C经过点
,且直线
,与圆
相切.
(1)求椭圆C的方程;
(2)直线
与椭圆C交于P,Q两点,点M在x轴上,且满足
,求点M横坐标的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
(1)求椭圆C的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53cd24fdb222c2e68c05c21600383df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db64a7467f0abcfe06cc9b279a5be7c.png)
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|
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3卷引用:山西省运城市稷山县稷王中学等3校2023届高三上学期期末数学试题
解题方法
4 . 已知双曲线
的左、右焦点分别为
,过
作圆
的切线,切点为
,延长
交双曲线
的左支于点
.若
,则双曲线
离心率的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b96eda0601673fafb836643969914f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2197b474d6cdef55a50b2d08753a102e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d48c79ce554b3968568a540b338439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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7卷引用:山西省运城市稷山县稷王中学等3校2023届高三上学期期末数学试题
山西省运城市稷山县稷王中学等3校2023届高三上学期期末数学试题山西省太原市2023届高三上学期期末数学试题(已下线)模块三 专题1 题型突破篇 小题入门夯实练(3)期末终极研习室(2023-2024学年第一学期)高三宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题(已下线)宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题(已下线)专题15圆锥曲线(选填题)(已下线)通关练16 双曲线13考点精练(100题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
5 . 如图,在三棱锥
中,平面
平面
,
,O为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/05da39df-3d0f-4c21-a917-59db0fd72ca1.png?resizew=187)
(1)证明:
;
(2)若
是边长为1的等边三角形,点E在棱
上,
,且二面角
的大小为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/05da39df-3d0f-4c21-a917-59db0fd72ca1.png?resizew=187)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bb2d945b7908ebac080e6595d4895f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d76c5ac5c9f0a2ec064487c02c476e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324d453870b345da0c41977290192f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
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|
350次组卷
|
2卷引用:山西省运城市稷山县稷王中学等3校2023届高三上学期期末数学试题
解题方法
6 . 已知抛物线
的焦点为
,过点
的直线交
于
两个不同点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/01c74a907dda6bb7d9d56d009d9df253.png)
A.若点![]() ![]() |
B.![]() |
C.若![]() ![]() ![]() |
D.过点![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
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2卷引用:山西省运城市稷山县稷王中学等3校2023届高三上学期期末数学试题
7 . 已知双曲线
的左、右焦点分别为
、
,且
,点
是双曲线第一象限内的动点,
的平分线交
轴于点
,
垂直于
交
于
,则以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.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/a2644e9f73e5871db934fdafc431d675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365e4d3b531424ccfd5a68c7975c7ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.当点![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
名校
8 . 如图,在圆柱
中,CE是圆柱的一条母线,ABCD是圆O的内接四边形,AB是圆O的直径,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/21/cbe55526-e380-44f7-a94c-04db8e6d2f05.png?resizew=137)
(1)若
,求证:
平面CEO;
(2)若
,求直线BE与平面ADE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/21/cbe55526-e380-44f7-a94c-04db8e6d2f05.png?resizew=137)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5edfe97aeab0cf16b40fa9d2e15f9e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba7be04bdcbb90d6b49ce9e14cda9bb.png)
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名校
解题方法
9 . 已知
为坐标原点,过点
的圆
与直线
:
相切,设圆心
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
的直线交曲线
于
、
两点,线段
的垂直平分线交
轴于点
,求
的面积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af74113f38fffeed8075e57d7f9d2533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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解题方法
10 . 已知抛物线
的焦点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/9c3a29c6-c76c-45ba-b61c-be95080b7958.png?resizew=167)
(1)如图所示,线段
为过点
且与
轴垂直的弦,动点
在线段
上,过点
且斜率为1的直线
与抛物线交于
两点,请问
是否为定值,若是,求出该定值;若不是,说明理由;
(2)过焦点
作直线
与
交于
两点,分别过
作抛物线
的切线,已知两切线交于点
,求证:直线
、
、
的斜率成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/9c3a29c6-c76c-45ba-b61c-be95080b7958.png?resizew=167)
(1)如图所示,线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8141a4a565a9b1e56bf710b84476a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6e75677951ef1388f76aee5a779149.png)
(2)过焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95add8635f609e7fdc0a423842f7d037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95add8635f609e7fdc0a423842f7d037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1ab8833d1823f3dc027a39bdb58e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1a6ce0b35896c8a1c687a4376e71f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75af77f184b8d76a881874298852081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ad3d1bc78e0ea7a5518f38c0cf5b30.png)
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|
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4卷引用:山西省运城市2022-2023学年高三上学期期末调研测试数学试题
山西省运城市2022-2023学年高三上学期期末调研测试数学试题山西省吕梁市2023届高三上学期期末数学试题(已下线)专题3 解答题题型(已下线)安徽省江南十校2022届高三下学期3月一模理科数学试题变式题16-20