解题方法
1 . 在直三棱柱
中,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/ffbf31c6-3e48-4e9b-83e9-9ee867196f60.png?resizew=114)
(1)求异面直线
所成角的余弦值;
(2)求直线
与平面
所成角的正弦值;
(3)求直线
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5448308469294d862f2c761ace330aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/ffbf31c6-3e48-4e9b-83e9-9ee867196f60.png?resizew=114)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881a85d9088d781ba1bec7ab3e02de49.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ce0eeb7a6d6c7806cf2352b9fe15c2.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ce0eeb7a6d6c7806cf2352b9fe15c2.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在四棱锥
,
平面
,底面
是直角梯形,其中
,
,
,
,
为棱
上的点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/e86845b6-fc97-4b95-a07d-635e5a66ae04.png?resizew=164)
(1)求证:
平面
;
(2)求平面
与平面
所成夹角的正弦值;
(3)求点
到平面
的距离.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfb2735e1683a6ae86b5b97a0032e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41744ec71119e7264ef9673a35805a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/e86845b6-fc97-4b95-a07d-635e5a66ae04.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
解题方法
3 . 已知椭圆
的左顶点为
,上顶点为
,离心率为
,
.
(1)求椭圆的方程;
(2)设点
在椭圆上,且异于椭圆的上、下顶点,点
在圆
上,直线
,
的斜率分别为
,
,且
,求证:
(i)
;
(ii)直线
过定点,并求出此定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
(1)求椭圆的方程;
(2)设点
![](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/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80b04ce48c9ace43276552c77108126.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d85c6b63bef0f632fee2e7e438a4b5cc.png)
(ii)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
解题方法
4 . 如图,
且
,
,
且
,
且
,
平面
,
,M为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/ead5b860-4040-40db-af0f-f38a12e0c74b.png?resizew=149)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f1161e0345b3646c71365430dccbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1989dc6aef61c294690d2105c72e894a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99188a6a00aabcd6936044139c771b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155de273b3d3857761ef315adb514b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7cb1376856b53c9d7a721dd92564f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cf187bc2ede965870b90757b495f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df76b0fddc037620e368d44cc30a791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/ead5b860-4040-40db-af0f-f38a12e0c74b.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0701f67727b0fc8100cfb5e20ec27d9b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0701f67727b0fc8100cfb5e20ec27d9b.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43819ab7b268a6293a9251935b594690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0701f67727b0fc8100cfb5e20ec27d9b.png)
您最近一年使用:0次
5 . 如图,在棱长为2的正方体
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/34441aed-3e4d-49d6-8091-33ef0c441207.png?resizew=167)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
和平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/34441aed-3e4d-49d6-8091-33ef0c441207.png?resizew=167)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea55a7e39361987096953d3a3ee1eaa4.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea55a7e39361987096953d3a3ee1eaa4.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea55a7e39361987096953d3a3ee1eaa4.png)
您最近一年使用:0次
名校
解题方法
6 . 设椭圆
的左、右焦点分别为
,左右顶点分别为
,已知椭圆
过点
,且长轴长为6.
(1)求椭圆
的标准方程;
(2)点
是椭圆
上一点(
不与顶点重合),直线
交
轴于点
,且满足
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46f04ec60daf12082dc3f1bf8d2e67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500272f9f312e2bc0f32e4afc058db41.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1dcef1a2703561586b4bd8f946cd41a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e5e3b13572a141ae74bfb65c925f19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
您最近一年使用:0次
2024-02-12更新
|
624次组卷
|
2卷引用:天津市五所重点校2023-2024学年高三上学期期末质量联合测试数学试题
7 . 设
,
两点的坐标分别为
,
.直线
,
相交于点
,且它们的斜率之积是
,记点
的轨迹为
.
(1)求
的方程
(2)设直线
与
交于
,
两点,若
的外接圆在
处的切线与
交于另一点
,求
的面积.
![](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/6fd0825e68122a65426840fbf07cf296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/ad3cd61d00f89e68ccca2cac5c937783.png)
您最近一年使用:0次
解题方法
8 . 如图,已知
平面
,
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/0a5d7a9b-1d84-43bf-8ffa-fadd382d50dd.png?resizew=159)
(1)求证:
平面
;
(2)求平面
与平面
的夹角的余弦值;
(3)求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/000a5d60075d7f1b9471cb12c18ebecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95ac28e265e944e323bed24e334969d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2220e68f9d97641a8074b1f7fe0a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10b66db4a8fbc6b0dc3dc160246b3533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb3a2b9ab304181ee5ff73b97a196ec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/0a5d7a9b-1d84-43bf-8ffa-fadd382d50dd.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a6ca1d6b37072bd7df0cf77737bb79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22ebcc4aa98d46366df48f751a5f368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
您最近一年使用:0次
9 . 已知椭圆
,
,
分别是椭圆C的左、右焦点,点
为左顶点,椭圆上的点到左焦点距离的最小值是焦距的
.
(1)求椭圆
的离心率;
(2)直线
过椭圆C的右焦点
,与椭圆C交于P,O两点(点P在第一象限).且
面积的最大值为
,
①求椭圆C的方程;
②若直线
,
分别与直线
交于
,
两点,求证:以
为直径的圆恒过右焦点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd3b3e802743d1c239c192c7fb8a599.png)
①求椭圆C的方程;
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c716601286ac3ef51a4c3c16b12e260.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
您最近一年使用:0次
解题方法
10 . 如图,正方形
与梯形
所在平面互相垂直,已知.
//
,
,
点P为线段EC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/8b134d4e-7962-42ff-9313-142637538d58.png?resizew=157)
(1)求证:
∥平面CDE;
(2)求直线DP与平面
所成角的正弦值;
(3)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987e2ad8478919f12a8cd0d7dd3309e5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/8b134d4e-7962-42ff-9313-142637538d58.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)求直线DP与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次