解题方法
1 . 已知椭圆
:
(
),四点
,
,
,
中恰有三点在椭圆
上.
(1)求椭圆
的标准方程.
(2)过点
的直线
与椭圆
交于不同的两点
,
,试问直线
,
的斜率之和是否为定值?若是定值,求出此定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5e70a5e3217b465248fe5556d43704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc3f28e53953c09fe49c4b9a21d732fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5982a89b1b83c6bbb635e35af01ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f951aa77fe06567532149782644fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a75aaf2b96de353cd12cc51f69e480.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392c373f9230552345b3f85a0f7f980b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcd5674420e9c9c40a035854ab31572.png)
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5卷引用:2023届青海省部分名校高三下学期适应性检测文科数学试题
名校
解题方法
2 . 设
分别是双曲线
的左、右焦点,过
作
的一条渐近线的垂线,垂足为
,若
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d943c426066938f0549852117d3eac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7卷引用:青海省西宁市大通回族土族自治县2023届高三第二次模拟理科数学试题
青海省西宁市大通回族土族自治县2023届高三第二次模拟理科数学试题青海省西宁市大通回族土族自治县2023届高三二模数学(理)试题河南省开封高级中学2022-2023学年高三下学期核心模拟卷(中)理科数学(四)试题(已下线)专题8-3 圆锥曲线小题综合 (讲+练)-2四川省内江市第六中学2022-2023学年高二下学期第二次月考数学(理)试题(已下线)第22讲 双曲线的简单几何性质9种常见考法归类(1)(已下线)专题04 双曲线15种常见考法归类(2)
解题方法
3 . 已知椭圆C:
的离心率为
,右焦点
与抛物线
的焦点重合.
(1)求椭圆C的方程;
(2)设椭圆C的左焦点为
,过点
的直线l与椭圆C交于
两点,A关于x轴对称的点为M,证明:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
(1)求椭圆C的方程;
(2)设椭圆C的左焦点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73609bec825b1b14eeb5bd11d66fe3f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/007b2cd470aaecd28839d8f778ae9dd2.png)
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5卷引用:青海省西宁市2023届高三一模理科数学试题
青海省西宁市2023届高三一模理科数学试题青海省西宁市2023届高三一模文科数学试题陕西省西安市周至县2023届高三下学期一模文科数学试题陕西省西安市周至县2023届高三下学期一模理科数学试题(已下线)重难点突破10 圆锥曲线中的向量问题(五大题型)
名校
4 . 如图,在三棱柱
中,
为边长为2的正三角形,D为
的中点,
,且
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/40bc791f-a3fd-4e66-a33e-e53aee3c4b57.png?resizew=181)
(1)证明:
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719de37e2bbf07a97de22f3353fabac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9bdbbdfabc737323692c796e41930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/40bc791f-a3fd-4e66-a33e-e53aee3c4b57.png?resizew=181)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/005c110169a6aa55414175b8e76fc9da.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46340bfad3505ef24f4916a61dd1a5e.png)
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3卷引用:青海省西宁市大通回族土族自治县2022-2023学年高三下学期开学摸底考试数学(理)试题
名校
解题方法
5 . 已知椭圆
的左右焦点分别为
,
,P是椭圆上任意一点,过
作
的外角平分线的垂线,垂足为Q,则Q与焦点间的最短距离为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/4466b55a-0306-400a-9b6d-e536710e0425.png?resizew=177)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b939a0c044b842cdc258e516a6d1de.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/4466b55a-0306-400a-9b6d-e536710e0425.png?resizew=177)
A.2 | B.1 | C.![]() | D.![]() |
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名校
6 . 如图,在四棱锥
中,平面
底面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/73513c62-b690-4ea7-bbbc-43d8ed238583.png?resizew=157)
(1)证明:
.
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2d817d2506f0f2e4a9926f9ba761cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d5fdc99dd2f51a7298c212745b7efc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/73513c62-b690-4ea7-bbbc-43d8ed238583.png?resizew=157)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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5卷引用:青海省西宁市六校联考2022-2023学年高三下学期开学考试数学(理)试题
7 . 如图,在三棱锥
中,平面
平面ABC,
,
,
,
,D是棱PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/14/6517ab49-40bf-423a-a02e-7159091f0c0e.png?resizew=167)
(1)求证:
;
(2)若
,求直线BC与平面ADB所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb8c91e4c85a9da7f54b2237d870a50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26a42b05e06fe34d66538930787bb3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e7f748d88b4eadfd1643c6b31fdf08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e766e52e5f64705a847ff1dbaba69c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/14/6517ab49-40bf-423a-a02e-7159091f0c0e.png?resizew=167)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e240a6378adf6d23ebf9cc710c9bd6.png)
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9卷引用:青海省玉树州2023届高三第三次联考数学理科试题
8 . 在直角梯形
(如图1),
,
,AD=8,AB=BC=4,M为线段AD中点.将△ABC沿AC折起,使平面ABC⊥平面ACD,得到几何体B-ACD(如图2).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/55a3ed2d-b40a-462d-a573-7243eab26dc9.png?resizew=332)
(1)求证:CD⊥平面ABC;
(2)求AB与平面BCM所成角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/55a3ed2d-b40a-462d-a573-7243eab26dc9.png?resizew=332)
(1)求证:CD⊥平面ABC;
(2)求AB与平面BCM所成角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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3卷引用:青海省西宁市海湖中学2023届高三下学期开学考试数学(理)试卷
9 . 已知抛物线
的焦点F到准线的距离为4,点
,
在抛物线C上,若
,则
( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d86fcb1e120228adc8a68023f2271e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99bffc6405a09ee6e48bdd8a225dc4ed.png)
A.4 | B.2 | C.![]() | D.![]() |
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13卷引用:青海省西宁市城西区青海湟川中学2022-2023学年高三上学期12月月考理科数学B试题
青海省西宁市城西区青海湟川中学2022-2023学年高三上学期12月月考理科数学B试题华大新高考联盟(全国卷)2023届高三上学期11月教学质量测评理科数学试题河南省南阳市第二完全学校高级中学2022-2023学年高三上学期12月月考数学试题(已下线)数学(乙卷理科)(已下线)数学(乙卷文科)四川省成都市第七中学2022-2023学年高三上期一诊模拟考试数学(文)试题四川省成都市第七中学2022-2023学年高三上期一诊模拟考试数学(理)试题四川省成都市2022-2023学年高三上学期12月一诊模拟数学(文)试题福建省厦门外国语学校石狮分校、泉港区第一中学两校2023届高三上学期第四次联考数学试题内蒙古赤峰实验中学、桥北四中2022-2023学年高三下学期大联考数学试题(理科)四川省仁寿第一中学校(北校区)2023届高三下学期2月月考文科数学试题四川省仁寿第一中学校(北校区)2023届高三下学期2月月考数学(理)试题(已下线)专题14 抛物线-1
名校
10 . 下列命题正确的是( )
A.“![]() ![]() |
B.若给定命题![]() ![]() ![]() ![]() |
C.若![]() |
D.命题“若![]() ![]() ![]() ![]() |
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