名校
解题方法
1 . 如图,三棱柱
中,D是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/03656881-a632-4480-aef3-10b67aaffd28.png?resizew=193)
(1)证明:
面
;
(2)若△
是边长为2的正三角形,且
,
,平面
平面
.求平面
与侧面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/03656881-a632-4480-aef3-10b67aaffd28.png?resizew=193)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)若△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad91719bd5fdc1b2d3d5298f2f44cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd426c9273efec5173db056d1d099f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
2020-08-17更新
|
1716次组卷
|
7卷引用:内蒙古呼和浩特市2020届高三第二次质量普查调研考试(二模)数学(理)试题
解题方法
2 . 在平面直角坐标系
中,直线
交椭圆
于两点
,
.
(1)若
,且点
满足
,证明:点
不在椭圆
上;
(2)若椭圆
的左,右焦点分别为
,
,直线
与线段
和椭圆
的短轴分别交于两个不同点
,
,且
,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125d7a3870ca37c558239a45214d3568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8868e2ba4401d727f1bcb1f5483b48f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aceb480e8dae1c574bc9f12540ef8561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e65748a485f2dd2be76ac64a370588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/0a60d05d3fec50690c2749ba07870441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea01a8d6d1251b1d5ae56a8fe076ce7.png)
您最近一年使用:0次
2020-06-13更新
|
230次组卷
|
2卷引用:四川省泸州市2020届高三第三次教学质量诊断性考试数学(理)试题
名校
解题方法
3 . 如图所示,在平行四边形ABCD中,
,
,
,点E是CD边的中点,将
沿AE折起,使点D到达点P的位置,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/27c77b74-f111-498c-8573-f114106a1da2.png?resizew=159)
(1)求证;平面
平面ABCE;
(2)求点E到平面PAB的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42ed2e5bd5a0f033e24008697bf4963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b43490ca09467a4c8cd8cfe91c94e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e99998f33ad6edab18180627d4903dcc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/27c77b74-f111-498c-8573-f114106a1da2.png?resizew=159)
(1)求证;平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d96357a07048ba79b8c84097d359d9.png)
(2)求点E到平面PAB的距离.
您最近一年使用:0次
2020-04-05更新
|
2282次组卷
|
4卷引用:内蒙古赤峰二中2020届普通高等学校招生第三次统一模拟考试理科数学试题
内蒙古赤峰二中2020届普通高等学校招生第三次统一模拟考试理科数学试题2019届四川省成都外国语学校高三一诊模拟考试数学(文)试题(已下线)考点27 空间向量求空间距离(讲解)-2021年高考数学复习一轮复习笔记广东省东莞市塘厦水霖学校2023-2024学年高二上学期段考一数学试题
名校
4 . 椭圆
:
的左、右焦点分别是
,
,离心率为
,左、右顶点分别为
,
.过
且垂直于
轴的直线被椭圆
截得的线段长为1.
(1)求椭圆
的标准方程;
(2)经过点
的直线与椭圆
相交于不同的两点
、
(不与点
、
重合),直线
与直线
相交于点
,求证:
、
、
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a9db3b2fef0dec32665bd83885fd58.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/860884c0017c8bceb5b0edff796c144f.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-04-22更新
|
297次组卷
|
2卷引用:2020届内蒙古呼伦贝尔市海拉尔区高三第一次统考文科数学试题
名校
解题方法
5 . 如图,过点
且平行与x轴的直线交椭圆
于A、B两点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/902dd0d0-4b0d-4b5e-86f0-94537b41ab94.png?resizew=236)
(1)求椭圆的标准方程;
(2)过点M且斜率为正的直线交椭圆于段C、D,直线AC、BD分别交直线
于点E、F,求证:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cda12642d59a5817e8990c43de20535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237f3e4b72fa5a52bccac514a5e52f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b7e59123eb43de595ff82d7ab4bde0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/902dd0d0-4b0d-4b5e-86f0-94537b41ab94.png?resizew=236)
(1)求椭圆的标准方程;
(2)过点M且斜率为正的直线交椭圆于段C、D,直线AC、BD分别交直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34fec6fc9de1cf94f1c367f3d79d6ed.png)
您最近一年使用:0次
2020-04-20更新
|
351次组卷
|
2卷引用:内蒙古通辽市蒙古族中学2020届高三模拟(六)数学(理)试卷
名校
6 . 如图,已知三棱柱
的侧棱与底面垂直,且
,
,
,
,点
,
,
分别为
、
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/979bd751-2b3f-4e8d-b527-f2f82fbba9f5.png?resizew=136)
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab926d89b65f26c12e3da73ef1e5cf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1192b3111a6dad01bba5227472bb4072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/979bd751-2b3f-4e8d-b527-f2f82fbba9f5.png?resizew=136)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5441a4e71b599d31c45940a7d2614f3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035544b514eb9802d433c8ece9909ea3.png)
您最近一年使用:0次
7 . 已知在平面直角坐标系中,动点P到定点F(1,0)的距离比到定直线x=-2的距离小1.
(1)求动点P的轨迹C的方程;
(2)若过点(1,0)的直线l与(1)中轨迹C交于A,B两点,通过A和原点O的直线交直线x=-1于D,求证:直线 DB平行于x轴.
(1)求动点P的轨迹C的方程;
(2)若过点(1,0)的直线l与(1)中轨迹C交于A,B两点,通过A和原点O的直线交直线x=-1于D,求证:直线 DB平行于x轴.
您最近一年使用:0次
2020-03-17更新
|
150次组卷
|
2卷引用:内蒙古赤峰市宁城县2019-2020学年高二上学期期末考试数学(文)试题
名校
解题方法
8 . 已知椭圆
:
的离心率为
.点
在椭圆
上,点
,
,
的面积为
,
为坐标原点.
(1)求椭圆
的标准方程;
(2)若直线
交椭圆
于
,
两点,直线
的斜率为
,直线
的斜率为
,且
,证明:
的面积是定值,并求此定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93c13c9d1a1f85ab7a9b044c669bf53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c240561788bc63f41a6703219fb66d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c09615735d331befd07664aa47cb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07729b1d25f39ebb2fcdd60dda091fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
2020-05-16更新
|
465次组卷
|
7卷引用:2020届陕西省西安市西北工业大学附中高三下学期4月适应性测试数学(理)试题
名校
9 . 已知点
在平行于
轴的直线
上,且
与
轴的交点为
,动点
满足
平行于
轴,且
.
(1)求出
点的轨迹方程.
(2)设点
,
,求
的最小值,并写出此时
点的坐标.
(3)过点
的直线与
点的轨迹交于
.
两点,求证
.
两点的横坐标乘积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b62ea7de9572d6c8e7fcdf03af761f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b96bdf51785d5d15292d6a194881ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a1bc4527c256cd1703da23af7b3acfb.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c9dcfd9f4c5298035870cb88a34169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7587d4dabcb349e848134753c3193f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1b3031d7393a63719166285314d73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d03310fa9440053c57d878acc06d02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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2020-01-01更新
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4卷引用:内蒙古鄂尔多斯衡水实验中学2019-2020学年第二学期高二数学理科期末考试试题
名校
10 . 在如图所示的四棱锥
中,四边形
是等腰梯形,
,
,
平面
,
,
.
(1)求证:
平面
;
(2)已知二面角
的余弦值为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5ba482836565abad208665cf7b9972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b5a90e556da12d63b7f481bd8e874c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b87b3be10408261827291574434d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7cad5d540488b66699a2cc72b882d8.png)
![](https://img.xkw.com/dksih/QBM/2020/4/22/2446941504200704/2447126916816896/STEM/fd016fdf3b164d6aaef98df88ba56e81.png?resizew=254)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)已知二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9d40f58f5fd5fb401a529a42b93ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138a5261a4cd0cb1f14b1dfccd4d916d.png)
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2020-04-22更新
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3卷引用:2020届内蒙古呼伦贝尔市海拉尔区高三第一次统考理科数学试题