名校
解题方法
1 . 已知圆
过点
,
,且圆心
在直线
上.
是圆
外的点,过点
的直线
交圆
于
,
两点.
(1)求圆
的方程;
(2)若点
的坐标为
,求证:无论
的位置如何变化
恒为定值;
(3)对于(2)中的定值,使
恒为该定值的点
是否唯一?若唯一,请给予证明;若不唯一,写出满足条件的点
的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02af485e17e7628fd5a3ace6e0a32ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.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/dad2a36927223bd70f426ba06aea4b45.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec40ff4479edca2ed18b6cadb8db72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
(3)对于(2)中的定值,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2023-10-01更新
|
596次组卷
|
7卷引用:福建省普通高中2021-2022学年高二1月学业水平合格性考试数学试题
福建省普通高中2021-2022学年高二1月学业水平合格性考试数学试题黑龙江省哈尔滨市第九中学校2022-2023学年高二10月月考数学试题福建省南安市柳城中学2022-2023学年高二上学期11月期中考试数学试题四川省通江中学2022-2023学年高二上学期期中文科数学试题专题08B圆的方程与圆锥曲线(已下线)重难点突破16 圆锥曲线中的定点、定值问题 (十大题型)-1(已下线)专题02 期中真题精选(压轴93题10类考点专练)(2)
2 . 给定正整数
,设集合
.对于集合M的子集A,若任取A中两个不同元素
,
,有
,且
,
,…,
中有且只有一个为2,则称A具有性质P.
(1)当
时,判断
是否具有性质P;(结论无需证明)
(2)当
时,写出一个具有性质P的集合A;
(3)当
时,求证:若A中的元素个数为4,则A不具有性质P.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2001591926ba62064d263796d1975085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5659bf1d65556a997fcf465153e87c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f2b8896c2e7bb71b704ecefe398e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3ac83d244c70c5162016ff68106212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11208b0364abf5391b6be25df50af30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e78346b2e8928ddf707b51f46c718ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee24dff02803ae6918cd45d39356a0f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c2bee43c4aaf6aeb901d7287dd339a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e788c32187ae2cc97aaa24da1d40d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbd5bb726a08c308b48373afebbb768.png)
您最近一年使用:0次
解题方法
3 . 阅读下面题目及其证明过程,在
处填写适当的内容.
已知三棱柱
,
平面
,
,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/daabe3a8-f5d5-4b94-9577-eeb61c3f5b0f.png?resizew=135)
(1)求证:
∥平面
;
(2)求证:
⊥
.
解答:(1)证明: 在
中,
因为
分别为
的中点,
所以 ① .
因为
平面
,
平面
,
所以
∥平面
.
(2)证明:因为
平面
,
平面
,
所以 ② .
因为
,
所以
.
又因为
,
所以 ③ .
因为
平面
,
所以
.
上述证明过程中,第(1)问的证明思路是先证“线线平行”,再证“线面平行”; 第(2)问的证明思路是先证 ④ ,再证 ⑤ ,最后证“线线垂直”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d5d02301554aad6cc89452c83f0862.png)
已知三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d77afb7d8280995886ff690e7a6c9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/daabe3a8-f5d5-4b94-9577-eeb61c3f5b0f.png?resizew=135)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
解答:(1)证明: 在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9e1e0d29bc4bdf0c6d38ca4db43343.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d77afb7d8280995886ff690e7a6c9a.png)
所以 ① .
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871502ee0c5d1414cfe81e8409b62d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f196748dc6a0d0bd9e9e4dd30ac4ed0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)证明:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be509ef5101aae24609ff9941cb246fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
所以 ② .
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
又因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d970e34169fb0de8a3f10e4c6ae40d.png)
所以 ③ .
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6cb3896ef1afc6a56a5aa0243022e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba985fb50a9078a839b66bf1d1eadea9.png)
上述证明过程中,第(1)问的证明思路是先证“线线平行”,再证“线面平行”; 第(2)问的证明思路是先证 ④ ,再证 ⑤ ,最后证“线线垂直”.
您最近一年使用:0次
解题方法
4 . 如图,在三棱柱
中,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/09199d19-bb37-40db-8607-6f6462bdcc0c.png?resizew=169)
(1)求证:
.
(2)若
为
的中点,问棱
上是否存在点
,使得
平面
?若存在,求出
的值,并给出证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d17d14819681c455a91d7678742368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a546cc14306823545141fd57225208ec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/09199d19-bb37-40db-8607-6f6462bdcc0c.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5ae8d145c5ce43e4cfc95fe6f563ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d109733379365295b93c58769d2019.png)
您最近一年使用:0次
5 . 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
6 . 如图,在直四棱柱
中,库面四边形
的对角线
,
互相平分,
为
的中点.
(1)求证:
平面
;
(2)若______,则平面
平面
.试在三个条件“①四边形
是平行四边形;②四边形
是矩形;③四边形
是菱形”中选取一个,补充在上面问题的横线上,使得结论成立,并证明.
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/2023/7/4/c80af623-5fef-41e1-98e0-00fd62c7b8de.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7542b49ab149f2be8ba6b48392bef1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)若______,则平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a46fbde58e12b1edc038ae9e921722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2020-09-21更新
|
1032次组卷
|
4卷引用:福建省普通高中2019-2020学年高二1月学业水平合格性考试数学试题
福建省普通高中2019-2020学年高二1月学业水平合格性考试数学试题福建省泉州市安溪第八中学2021届高三学业合格模拟检测(一)数学试题人教A版(2019) 必修第二册 实战演练 第八章 验收检测(已下线)第8章 立体几何初步(单元提升卷)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)
7 . 对于给定的抛物线
,使得实数p、q满足
.
(1)若
,求证:抛物线
与x轴有交点.
(2)证明:抛物线
的最大值大于等于抛物线
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d972cf8c74b5218298b60908716a8d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c059fce1db054ebb94902a84d25fcd43.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e864b9d4b6a0aa76416348778b26d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2630d6cf14b3e8c82ee7080799901b8d.png)
(2)证明:抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bee92cd110cd46e04633e18c17c4b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188f03bd3b6ee375cbc88926cfbcd774.png)
您最近一年使用:0次
解题方法
8 . 已知
是常数,在数列
中,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94ae936f82425aadd82bfbc76079d2a.png)
(1)若
,求
的值;
(2)若
=4,证明:数列
是等比数列,并求数列
的通项公式;
(3)在(2)的条件下,设数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94ae936f82425aadd82bfbc76079d2a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)在(2)的条件下,设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1302abaebc9df026c2a83291063e83b4.png)
您最近一年使用:0次
9 . 如图,四棱锥
中,底面
是正方形,
平面
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
平面
;
(2)证明:平面
平面
.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d4c42112e0a22f240ce2ae432e5b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2016-12-04更新
|
617次组卷
|
7卷引用:2015-2016学年湖南省衡阳一中高二下学业水平模拟数学试卷(1)