1 . 已知过原点的三条直线与抛物线
:
依次交于
,
,
三点,同样这三条直线与抛物线
:
依次交于
,
,
三点.
(1)试判断直线
与
的位置关系,并证明;
(2)试判断
与
的面积比是否为定值,若是求出此定值,若不是请说明理由;
(3)若
与
都与抛物线
:
相切,求证
也和
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)试判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34876d748f30fa4fc2eb6a686b5ff5.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828dc8dc7259c510b6d63abf40f60e90.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4dbe5d5c8b9c28c6f5eb92278a9f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4dbe5d5c8b9c28c6f5eb92278a9f17.png)
您最近一年使用:0次
2 . 如图,在三棱锥
中,平面
平面
,
,
为
中点且
.
(1)求证:
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7b2de299e42614a40b72b3126c3e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5f0e2cc2158bd508edd68e05a892b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/5/1d7ad316-503e-4255-9599-a95289ea3952.png?resizew=133)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed46a014ece6a0830c7c8b8deb2c56e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
解题方法
3 . 如图,正三棱柱
中,
分别是棱
上的点,
.点M为棱
上的动点,满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/0efce3ec-061b-4193-afd2-e9942d9c847a.png?resizew=145)
(1)当
为何值时,直线
平面
,并证明你的结论;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c95c0160e73beb94a4a1cbc0168e9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e80c9702720a88f4a31c0484c7ff5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172445f5dadf958310b11a6b970bc05b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/0efce3ec-061b-4193-afd2-e9942d9c847a.png?resizew=145)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98dbbf1a30ea54a46b903a9645debab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d557872d3299577be8c5872ba1ae5b59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8762b26b773a3c41e51d1eb3113169.png)
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解题方法
4 . 已知直三棱柱
,各棱长均为
,
为
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2023/6/19/3262952090034176/3265184698048512/STEM/6451cd34d1f54fa8b00c8cc0b7e95186.png?resizew=178)
(1)求直三棱柱
的体积;
(2)求证:
平面
;
(3)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2023/6/19/3262952090034176/3265184698048512/STEM/6451cd34d1f54fa8b00c8cc0b7e95186.png?resizew=178)
(1)求直三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42605242ae45b6223b23b7a70a2b1618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
(3)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
您最近一年使用:0次
5 . 如图所示,在四棱锥
中,
平面ABCD,四边形ABCD是矩形,且
,
,E是棱BC上的动点,F是线段PE的中点.
平面ADF;
(2)若直线DE与平面ADF所成的角为30°,求EC的长.
![](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/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
(2)若直线DE与平面ADF所成的角为30°,求EC的长.
您最近一年使用:0次
名校
6 . 如图,四棱锥
的底面
为平行四边形,
是边长为
的等边三角形,平面
平面
,
,
,点
是线段
上靠近点
的三等分点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/9bbf75ec-86f5-4976-b078-4d659a9dab48.png?resizew=171)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4edc320c5767838e1761c189b6c48a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9880952857950577055578875ab29141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553d5269397c5cf0909c734464e1b472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dbacc8f5a9d6c606548dc11f19781e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19e44711cb887515d7f75e73845c175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/9bbf75ec-86f5-4976-b078-4d659a9dab48.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c17cbe2d45c8da02c0cb80bf407da9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-10-24更新
|
756次组卷
|
11卷引用:江西省南昌市2017届高三第三次模拟考数学(理)试题
江西省南昌市2017届高三第三次模拟考数学(理)试题江西省南昌市2017届高三第三次模拟考理科数学试题【全国百强校】浙江省宁波市镇海中学2019届高三上学期期中考试数学试题浙江省杭州市北斗联盟2019-2020学年高二下学期期中联考数学试题浙江省杭州市富阳区第二中学2020-2021学年高二下学期4月月考数学试题浙江大学附属中学玉泉校区2021-2022学年高二下学期期中数学试题江西省南昌市新建区第二中学2022-2023学年高二上学期10月学业水平考核数学试题广西壮族自治区南宁高新技术产业开发区桂鼎学校2022-2023学年高二上学期11月期中数学试题山西省阳泉市第一中学校2022-2023学年高三上学期11月期中考试数学试题专题07B立体几何解答题山西省大同市云冈区汇林中学2024届高三上学期期中数学试题
解题方法
7 . 已知椭圆
:
的离心率为
,且经过点
.
(1)求
的方程;
(2)过椭圆
外一动点
作椭圆
的两条切线
,
,斜率分别为
,
,若
恒成立,证明:存在两个定点,使得点
到这两定点的距离之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/4f6d6a0ee7672e93d79d51b938d9299e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解题方法
8 . 如图所示,在四棱锥
中,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/10/d3b09640-c5ff-4e08-8f27-e552451ebf97.png?resizew=171)
(1)证明:
;
(2)若四棱锥
的体积为4,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/f01eb0397a65f3a2a928b7ea77ce3e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/10/d3b09640-c5ff-4e08-8f27-e552451ebf97.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9104a1941e557a85fd1496bc2b9be297.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
解题方法
9 . 如图,在三棱锥
中,
平面
,点
分别是
和
的中点,已知
,直线
与平面
所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/20/349452a3-7825-4485-9588-5f6858bb0f80.png?resizew=187)
(1)求证:平面
平面
:
(2)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6deecf9ccb7b7879455050633219e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffbc423070f5d7ce2c72229066ee1cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d553f8d549f8ff2e9abca41cc1741c4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/20/349452a3-7825-4485-9588-5f6858bb0f80.png?resizew=187)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c54a3c4557148887b49591696a831e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e9ac46aabe38e5ea1a8cb0febc98af.png)
您最近一年使用:0次
2022-08-18更新
|
681次组卷
|
2卷引用:重庆市2021-2022学年高一下学期学业质量调研数学试题
解题方法
10 . 如图,三棱柱
的底面
为菱形,
,
为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/56d2d9f2-48d1-4694-8bc6-03fec6ad60df.png?resizew=177)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4453f2455405aefb4e1ff34b2304abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3620fb6546354672bdea07a30e0b0e17.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/56d2d9f2-48d1-4694-8bc6-03fec6ad60df.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8c10f56d59217c8c1a650224278b87.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8c10f56d59217c8c1a650224278b87.png)
您最近一年使用:0次