1 . 已知
是椭圆
的右焦点,过点
的直线交椭圆于
两点.
是
的中点,直线
与直线
交于点
.
(Ⅰ)求证:
;
(Ⅱ)求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57578d58a051ec128f76a48b41091b31.png)
(Ⅱ)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22bca838bac6ba107da9c05705e93bc.png)
您最近一年使用:0次
2019-05-12更新
|
969次组卷
|
3卷引用:【市级联考】新疆乌鲁木齐地区2019届高三第三次质量检测(文)数学试题
【市级联考】新疆乌鲁木齐地区2019届高三第三次质量检测(文)数学试题2019届新疆乌鲁木齐地区高三第三次质量检测数学(理)试题(已下线)专题08 解析几何中的最值范围问题(第五篇)-备战2020年高考数学大题精做之解答题题型全覆盖
2 . 如图,在四棱锥
中,底面
是菱形,
平面
,且
,点
,
分别是
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/dc97f9da-be6f-420e-928c-912510447827.png?resizew=222)
(Ⅰ)求证
平面
;
(Ⅱ)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/efdf3b093c42cd20c819e0d7ea93f3cd.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/dc97f9da-be6f-420e-928c-912510447827.png?resizew=222)
(Ⅰ)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864689852707154e3a9be79f657f16d4.png)
您最近一年使用:0次
2019-03-19更新
|
408次组卷
|
2卷引用:【市级联考】新疆乌鲁木齐市2019届高三第二次诊断性测试数学(理)试题
3 . 已知拋物线C:
经过点
,其焦点为F,M为抛物线上除了原点外的任一点,过M的直线l与x轴、y轴分别交于A,B两点.
Ⅰ
求抛物线C的方程以及焦点坐标;
Ⅱ
若
与
的面积相等,证明直线l与抛物线C相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940349e98dc700cb6e196879c1a5ad72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e15e83c607c1c733d34df1f52e40d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8858a6a17aab0404023a9fa2ae9a5e3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afac6934256a23613443c393446881a4.png)
您最近一年使用:0次
2019-04-16更新
|
826次组卷
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4卷引用:【市级联考】新疆乌鲁木齐2019届高三第二次质量检测文科数学试题
【市级联考】新疆乌鲁木齐2019届高三第二次质量检测文科数学试题【市级联考】新疆乌鲁木齐地区2019届高三第二次质量监测数学(理)试题2019届新疆乌鲁木齐地区高三第二次质量监测数学(文)试题(已下线)湖南省株洲市2023届高三下学期一模数学试题变式题17-22
4 . 如图,在四棱锥
中,平面
平面BCDE,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/5cf54a92-71f2-4e18-a39e-21016bd42a20.png?resizew=126)
求证:
平面ABC;
求平面ABE与平面ADC所成二面角大小的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5950b2be8b3a4cef62580f73f7e2f778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99bfa2ca4e398c8ab0f97f47add3754f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265ad748834e159aaeeb9e4e7ccc294b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc219dbd7f28fc44d8dab340ff4b5c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b77d1a22977ce5f43d36e40b648bd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef27ae2e2bd091fa0879d0ea96c6d1e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/5cf54a92-71f2-4e18-a39e-21016bd42a20.png?resizew=126)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd244dd270528347a22d8101ac73726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
您最近一年使用:0次
5 . 如图,
和
所在平面互相垂直,且
,
,
、
分别为
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/35156ea3-b3c6-4a59-b1fe-0ffcf9329be5.png?resizew=169)
(1)求证:
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df6d51738ac1bc8b9530ea4a55745c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762cd2d2e0550938fe77347b4a3a42ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d33b11489be0d7f7ec786fb04907c3c.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/35156ea3-b3c6-4a59-b1fe-0ffcf9329be5.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41861a8201bf8378a05a09ae0bd84635.png)
您最近一年使用:0次
6 . 已知椭圆
的中心在原点,
是它的一个焦点,直线
,过点
与椭圆
交于
,
两点,当直线
轴时,
.
(1)求椭圆
的标准方程;
(2)设椭圆的左顶点为
,
、
的延长线分别交直线
于
,
两点,证明:以
为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dd42188ae3b66affd240183dd395c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6cf7df967a6fbf596dbe7914537d7c5.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设椭圆的左顶点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ea9f5967c96e60f03f332fd792cd21.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/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2019-03-10更新
|
576次组卷
|
3卷引用:【省级联考】新疆维吾尔自治区2019届高三普通高考第一次适应性检测理科数学试题
名校
7 . 椭圆
的中心在坐标原点,焦点在坐标轴上,过
的长轴,短轴端点的一条直线方程是
.
(1)求椭圆
的方程;
(2)过点
作直线交椭圆
于
,
两点,若点
关于
轴的对称点为
,证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1095552cc653b6c456d4021bab926d95.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d059a0d71bddb677c603d84fac444b.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
您最近一年使用:0次
2019-03-18更新
|
791次组卷
|
5卷引用:【市级联考】新疆乌鲁木齐市2019届高三一模试卷(理科)数学试题
【市级联考】新疆乌鲁木齐市2019届高三一模试卷(理科)数学试题【市级联考】新疆乌鲁木齐市2019届高三一模试卷(文科)数学试题(已下线)2022年全国高考乙卷数学(理)试题变式题13-16题(已下线)2022年全国高考乙卷数学(理)试题变式题17-20题河南省济源市第四中学2022-2023学年高二上学期1月份月考理科数学试题
2010·福建南平·一模
8 . 如图,在三棱锥
中, 侧面
与侧面
均为等边三角形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f809f9d492d97cb06e49af3a5d36ab.png)
为
中点.
(Ⅰ)证明:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f390394bb231e1d0c4708976b4b370.png)
(Ⅱ)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f809f9d492d97cb06e49af3a5d36ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d30637da200a07672ae231b4c5c09cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f390394bb231e1d0c4708976b4b370.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8f249c2bec5e988d4b1d233c80c5b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/2e4e3103-6904-4751-b8d8-3ac0708761dc.png?resizew=169)
您最近一年使用:0次
2019-01-30更新
|
2798次组卷
|
20卷引用:2011届新疆农七师高级中学高三第二次模拟考试数学理卷
(已下线)2011届新疆农七师高级中学高三第二次模拟考试数学理卷(已下线)2010-2011学年新疆乌鲁木齐八中高二下学期期末考试理科数学(已下线)2013届新疆乌鲁木齐市第八中学高三第一次月考数学试卷新疆玛纳斯县第一中学2021届高三上学期期中备考2数学(理)试题(已下线)福建省南平市2010年高中毕业班适应性考试数学试题(理科)2007年普通高等学校招生全国统一考试理科数学卷(海南)(已下线)2011届福建省古田一中高三上学期期中考试数学理卷(已下线)2011届福建省古田一中高三上学期期中考试数学文卷2014-2015学年湖北武汉部分重点中学高二下期末考试理科数学试卷2019届百师联盟全国高三冲刺考(三)全国卷文科数学试卷2020届山西省太原市第五中学高三第二次模拟(6月) 数学(理)试题山西省太原五中2020届高三高考数学(理科)二模试题湖南省邵阳市邵东县第一中学2019-2020学年高二下学期期末数学试题陕西省汉中市洋县第一中学2019-2020学年高二上学期期中数学试题陕西省西安交大附中2019-2020学年高一上学期12月月考数学试题黑龙江省大庆中学2021-2022学年高三上学期开学考试数学(理)试题上海市复兴高级中学2022届高三下学期3月练习数学试题陕西省榆林市绥德中学2021-2022学年高二下学期第一次阶段性测试理科数学试题福建省龙岩市上杭县第二中学2021-2022学年高二5月月考数学试题2007年普通高等学校招生考试数学(理)试题(琼、宁卷)
9 . 已知椭圆
过点
,其长轴、焦距和短轴的长的平方依次成等差数列
直线l与x轴正半轴和y轴分别交于点Q、P,与椭圆分别交于点M、N,各点均不重合且满足
.
求椭圆的标准方程;
若
,试证明:直线l过定点并求此定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fef9380b394a4bd829c83a5a5b4c859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d72c5b96cb21f8303cf604586efa601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b13c4f91e8f154babede95f37ac0302.png)
您最近一年使用:0次
2019-03-27更新
|
1404次组卷
|
3卷引用:【省级联考】新疆2019届高三年级第一次毕业诊断及模拟测试文科数学试题
10 . 在平面直角坐标系
中,
是
轴上的动点,且
, 过点
分别作斜率为
,
的两条直线交于点
,设点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
的两条直线分别交曲线
于点
和
,且
,求证直线
的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad57e3727b7bbd795b05332fbf9649e9.png)
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2018-08-01更新
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3卷引用:2017届新疆乌鲁木齐市高三下学期第三次诊断性测验(三模)数学(理)试卷
2017届新疆乌鲁木齐市高三下学期第三次诊断性测验(三模)数学(理)试卷【全国百强校】河北省武邑中学2018届高三下学期第五次模拟考试数学(理)试题(已下线)必刷卷04-2021年高考数学(文)考前信息必刷卷(新课标卷)