1 . 已知动点
(其中
)到定点
的距离比点
到
轴的距离大1.
(1)求点
的轨迹
的方程;
(2)过椭圆
的右顶点作直线交曲线
于
、
两点,其中
为坐标原点
①求证:
;
②设
、
分别与椭圆相交于点
、
,证明:原点到直线
的距离为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070e07dc652add7047281a69502a1b8b.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/1dde8112e8eb968fd042418dd632759e.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
2020-11-03更新
|
1221次组卷
|
7卷引用:吉林省抚松县第一中学2021-2022学年高二下学期开学考试数学试题
吉林省抚松县第一中学2021-2022学年高二下学期开学考试数学试题山东省烟台莱阳市第一中学2021-2022学年高二下学期开学摸底考试数学试题(已下线)【新教材精创】2.8+直线与圆锥曲线的位置关系(2)-B提高练-人教B版高中数学选择性必修第一册四川省成都市蓉城名校联盟2020-2021学年高三第一次联考理科数学试题(已下线)专题9.8 《平面解析几何》单元测试卷(测)-2021年新高考数学一轮复习讲练测(已下线)专题9.8 《平面解析几何》单元测试卷-2021年新高考数学一轮复习学与练(已下线)第五篇 向量与几何 专题8 帕斯卡定理、布列安桑定理、笛沙格定理、彭塞列闭合定理 微点3 笛沙格定理、彭塞列闭合定理
2 . 如图,在四棱锥
中,
平面ABCD,底面ABCD为正方形,
,E,F分别为PD,PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/0bd44357-ca0f-45c5-8a87-77a82472215e.png?resizew=143)
(1)求证:
平面PAD;
(2)求平面AEF与底面ABCD所成角的余弦值.
![](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/c3b10835116b9b777a666b438c907b49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/0bd44357-ca0f-45c5-8a87-77a82472215e.png?resizew=143)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
(2)求平面AEF与底面ABCD所成角的余弦值.
您最近一年使用:0次
名校
3 . 如图,等腰直角,
,
,
、
分别为
、
中点,将
沿
翻折成
,得到四棱锥
,
为
中点.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53569e6ec795658b4fffcddeebe0f142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739ad948445af72d585fe29c745929b.png)
您最近一年使用:0次
2023-08-25更新
|
766次组卷
|
4卷引用:吉林省长春市长春净月高新技术产业开发区东北师范大学附属中学2022-2023学年高二上学期期中数学试题
吉林省长春市长春净月高新技术产业开发区东北师范大学附属中学2022-2023学年高二上学期期中数学试题(已下线)第3章 空间向量及其应用 单元综合检测(重点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)专题05 直线与平面的夹角4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)(已下线)考点巩固卷18 空间向量与立体几何(九大考点)
名校
解题方法
4 . 如图,在正三棱柱
中,
,点
在
上,且
,
为
中点,证明:
(1)
平面
;
(2)平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baa3d0db9ad31d33c2883a6efed1dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cd21f01a0ff0a12dcd8c3e40ff5f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/26/61161d54-a52f-445f-9839-39ddb3cb1b8e.png?resizew=159)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde9b576a6b6e6d56e92f75e9c01a4f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07a33bc93519e73c348079a3fdf90af.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a7daa3e613b36ed510a93bce3be664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07a33bc93519e73c348079a3fdf90af.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,四棱锥
中,
,
,
,
,
,
为线段
中点,线段
与平面
交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/27/f5fb60cd-f205-47d6-b4ca-6b8ded0f0c2e.png?resizew=197)
(1)证明:平面
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1bfda3eb47e76080a877533deb072b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cd8ba7eb52e38857830162e770f534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/27/f5fb60cd-f205-47d6-b4ca-6b8ded0f0c2e.png?resizew=197)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
(3)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c5db0d86500773db74278f092f3d78.png)
您最近一年使用:0次
2023-08-25更新
|
1105次组卷
|
3卷引用:吉林省长春市长春净月高新技术产业开发区东北师范大学附属中学2022-2023学年高二上学期期中数学试题
吉林省长春市长春净月高新技术产业开发区东北师范大学附属中学2022-2023学年高二上学期期中数学试题(已下线)专题03 空间向量求角度与距离10种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)(已下线)难关必刷01 空间向量的综合应用-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
6 . 已知抛物线
的焦点为
,
为抛物线上一点,
,且
的面积为
,其中
为坐标原点.
(1)求抛物线
的方程;
(2)已知点
,不垂直于
轴的直线
与抛物线
交于
,
两点,若直线
,
关于
轴对称,求证:直线
过定点并写出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6595367508aef224945bb140eae7bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0942fc5e4da4ae86721efc5bb7e2cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23728b4c0467a27d90f71b424f6a946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-02-19更新
|
450次组卷
|
5卷引用:吉林省白城市通榆县2022-2023学年高二上学期期末数学试题
7 . 已知椭圆
的左顶点为
,点
在椭圆
上,且
.
(1)求椭圆
的标准方程.
(2)设过点
的直线
与椭圆
交于
(异于
两点)两点,直线
,
分别与
轴交于
三点.证明:
是线段
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa6d8c9ab3d942b005965bc18dbf5ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51fba53eb5c845768f7c28cec52360cb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3524267234fd8d7277343ac9796b314.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f6be6c2edc0699b9a6fe549fda5bebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9eec500e0ebf0918587ca06da1edd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19247393d6b9122742a1a926ff495314.png)
您最近一年使用:0次
2022-11-16更新
|
393次组卷
|
3卷引用:吉林省吉林市等2地2022-2023学年高二上学期期中联考数学试题
8 . 如图,在四棱锥
中,
平面
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/9c8fe745-7a33-44eb-9ea0-0090520280f0.png?resizew=171)
(1)证明:
平面
.
(2)若
,点
在棱
上,求平面
与平面
夹角的余弦值的最小值.
![](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/728fcb9b078221a54ca841145ab93227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/9c8fe745-7a33-44eb-9ea0-0090520280f0.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee90881c743e2cff2e3128d6bdb86174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2022-11-16更新
|
412次组卷
|
3卷引用:吉林省吉林市等2地2022-2023学年高二上学期期中联考数学试题
名校
9 . 如图,在直四棱柱
中,底面
是正方形,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/6e2da271-a43f-4ef2-8a3b-d4249c10ad3a.png?resizew=140)
(1)证明:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f21c7c194c5bc2986a21fd441c81495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/6e2da271-a43f-4ef2-8a3b-d4249c10ad3a.png?resizew=140)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd823da794135c17889c2a2d42d0a149.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd823da794135c17889c2a2d42d0a149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea55a7e39361987096953d3a3ee1eaa4.png)
您最近一年使用:0次
2023-01-16更新
|
228次组卷
|
3卷引用:吉林省白城市通榆县2022-2023学年高二上学期期末数学试题
名校
解题方法
10 . 如图,在边长为2的正方体
中,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/543dba1f-4a3a-4442-9648-7a8a1a1a4028.png?resizew=145)
(1)证明:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d572fdea0ba4336ccf77c76db7f0332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e5ee662272a9cda713dcff67f57155.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/543dba1f-4a3a-4442-9648-7a8a1a1a4028.png?resizew=145)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae15ccbbb50c42c05ad50bcfa63e85dd.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
您最近一年使用:0次
2022-09-28更新
|
1658次组卷
|
7卷引用:吉林省长春外国语学校2022-2023学年高二上学期第一次月考数学试题