解题方法
1 . 已知椭圆
的中心为坐标原点
,焦点在
轴上,离心率为
,
分别为椭圆
的左、右焦点,点
在椭圆
上,以线段
为直径的圆经过点
,线段
与
轴交于点
,且
.
(1)求椭圆
的方程;
(2)设动直线
与椭圆
交于
两点,且
.求证:动直线
与
圆相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da01a3abe1c9dc4e6283afa0dc1a0d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f2188d99b44972f1e13d3a339ee5c7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设动直线
![](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/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2abe13e2d4176f55f71677bbbb6eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2845cff59808d0945644a6c867e40740.png)
您最近一年使用:0次
名校
解题方法
2 . 在三棱锥
中,
,则三棱锥
的外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42a632036951c49402fe0ccc30d2183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2018-03-04更新
|
2050次组卷
|
4卷引用:专题7-1 立体几何压轴小题:截面与球(讲+练)-1
(已下线)专题7-1 立体几何压轴小题:截面与球(讲+练)-1(已下线)专题17 球面几何(外接球、内切球和棱切球)-3广东省深中、华附、省实、广雅四校2018届高三模拟联考理科数学试题人教A版高一数学必修2第一章《空间几何体》专题检测
3 . 如图所示,在平面直角坐标系
中,第一象限内有定点
和射线
,已知
,
的倾斜角分别为
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8022567f649e454aa2531578a853786c.png)
轴上的动点
与
,
共线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/fa2625a0-e384-4b3d-9260-1a58cf768dd0.png?resizew=165)
(1)求
点坐标(用
表示);
(2)求
面积
关于
的表达式
;
(3)求
面积的最小时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536e072eb0439a5e5b430cd55a129374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7951e46b0523ad36e274190cbac74a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8022567f649e454aa2531578a853786c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79c41d77ce318543dbe54ca70bcc08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/fa2625a0-e384-4b3d-9260-1a58cf768dd0.png?resizew=165)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edafce95aade0386bc0d78f679dcf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa34879524083345a66ff93f6e75c583.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edafce95aade0386bc0d78f679dcf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
名校
解题方法
4 . 把平面图形
上的所有点在一个平面上的射影构成的图形
叫做图形
在这个平面上的射影.如图,在三棱锥
中,
,
,
,
,
,将围成三棱锥的四个三角形的面积从小到大依次记为
,
,
,
,设面积为
的三角形所在的平面为
,则面积为
的三角形在平面
上的射影的面积是
![](https://img.xkw.com/dksih/QBM/2017/3/28/1653753087377408/1656596902756352/STEM/07c1669bb07b4feb900e77cb2c3a00f2.png?resizew=286)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7796caec20ab20a46b31f36a188392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73cab28475a885ff0b5b5d947d65b5ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8739cc8fc1570400f30f5af109a025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a1100f8c8bd07c7dfc3c29991acf00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca201616362528f3615de6edb2317848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56d35b0e69e306a453c5226899c71c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d43eb0b274e00cbbc4a210da4165042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530f5b63e797195906285c0c03eb9276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c2d5971afbff8eca1b9aff5f76f710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e204eeda3cbe67e9e709be5c790b49f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530f5b63e797195906285c0c03eb9276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e204eeda3cbe67e9e709be5c790b49f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/2017/3/28/1653753087377408/1656596902756352/STEM/07c1669bb07b4feb900e77cb2c3a00f2.png?resizew=286)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2017-04-01更新
|
1850次组卷
|
6卷引用:专题8.6 空间直线、平面的垂直(一)【八大题型】-举一反三系列
(已下线)专题8.6 空间直线、平面的垂直(一)【八大题型】-举一反三系列2017届四川省成都市高三第二次诊断性检测数学理试卷河北省衡水市衡水中学2019届高三下学期六调考试(文)数学试题(已下线)【全国百强校】河北省衡水中学2019届高三下学期六调考试数学(文)试题四川省泸县第五中学2022-2023学年高三上学期第三学月考试数学(理)试题重庆市万州第二高级中学2023届高三三诊数学试题
真题
名校
5 . 如图,已知曲线
,曲线
,P是平面上一点,若存在过点P的直线与
都有公共点,则称P为“C1—C2型点”.
(1)在正确证明
的左焦点是“C1—C2型点”时,要使用一条过该焦点的直线,试写出一条这样的直线的方程(不要求验证);
(2)设直线
与
有公共点,求证
,进而证明原点不是“C1—C2型点”;
(3)求证:圆
内的点都不是“C1—C2型点”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f63dee0fb484e63eb3a8baebcdf46f1.png)
![](https://img.xkw.com/dksih/QBM/2013/7/18/1571296931315712/1571296936722432/STEM/3ed6c0368dc94e10afd48a28c75e801f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/30/854d5f50-0404-48a2-ba83-49ad3c2727e1.png?resizew=168)
(1)在正确证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553288bc51ba6174dab2e0175d2df90a.png)
(3)求证:圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28123e129b6426c9a5f31ad8ec2465b.png)
您最近一年使用:0次
2019-01-30更新
|
2080次组卷
|
6卷引用:沪教版(上海) 高三年级 新高考辅导与训练 第二部分 走近高考 第十一章 圆锥曲线高考题选
名校
6 . 已知圆C:x2+(y-3)2=2,点A是x轴上的一个动点,AP,AQ分别切圆C于P,Q两点,则线段PQ的取值范围是
A.[![]() ![]() | B.[![]() ![]() | C.[![]() ![]() | D.[![]() ![]() |
您最近一年使用:0次
2018-12-12更新
|
1118次组卷
|
5卷引用:考点8-1 直线与圆(文理)
(已下线)考点8-1 直线与圆(文理)(已下线)专题09 直线与圆(已下线)专题1 直线与圆的位置关系【练】(压轴小题大全)【全国百强校】江苏省启东中学2018-2019学年高一上学期第二次月考数学试题2四川省绵阳南山中学2021-2022学年高三上学期12月月考数学(文)试题
7 . 在平面直角坐标系
中,原点为
,抛物线
的方程为
,线段
是抛物线
的一条动弦.
(1)求抛物线
的准线方程和焦点坐标
;
(2)当
时,设圆
:
,若存在两条动弦
,满足直线
与圆
相切,求半径
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ed9d97b8745ed1c15349ea3fffc299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d27eb9f313d561b0e9073b51af83d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
名校
8 . 如果四面体的四条高交于一点,则该点称为四面体的垂心,该四面体称为垂心四面体.
(1)证明:如果四面体的对棱互相垂直,则该四面体是垂心四面体;反之亦然.
(2)给出下列四面体
①正三棱锥;
②三条侧棱两两垂直;
③高在各面的射影过所在面的垂心;
④对棱的平方和相等.
其中是垂心四面体的序号为 .
(1)证明:如果四面体的对棱互相垂直,则该四面体是垂心四面体;反之亦然.
(2)给出下列四面体
①正三棱锥;
②三条侧棱两两垂直;
③高在各面的射影过所在面的垂心;
④对棱的平方和相等.
其中是垂心四面体的序号为 .
您最近一年使用:0次
11-12高三·上海·阶段练习
9 . 对于函数
,若存在实数
,使
成立,则称
为
的不动点.
(1)当
时,求
的不动点;
(2)若对于任意的实数
函数
恒有两个相异的不动点,求实数
的取值范围;
(3)在(2)的条件下,若
的图象上
两点的横坐标是函数
的不动点,且直线
是线段
的垂直平分线,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf74824de75eb9090f23aba760eeaf52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbf1211335bcbc0ebb05414669eda0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c80438b35c093c2de9dce83c650ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbf1211335bcbc0ebb05414669eda0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175cb11352db7903799db939b29c5c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
(2)若对于任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ed049f8d33b7ce57556820a68c1830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7062416ad3bd49f76ac3f43df41575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768c20053807a4bd8caac91e4912191f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
名校
10 . 已知点P和非零实数
,若两条不同的直线
均过点P,且斜率之积为
,则称直线
是一组“
共轭线对”,如直
是一组“
共轭线对”,其中O是坐标原点.
是一组“
共轭线对”,求
的夹角的最小值;
(2)已知点A(0,1)、点
和点C(1,0)分别是三条直线PQ,QR,RP上的点(A,B,C与P,Q,R均不重合),且直线PR,PQ是“
共轭线对”,直线QP,QR是“
共轭线对”,直线RP,RQ是“
共轭线对”,求点P的坐标;
(3)已知点
,直线
是“
共轭线对”,当
的斜率变化时,求原点O到直线
的距离之积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5883f18fe46765e94aba381bff58d501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120be1fe068d0caeb470903565101d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf497f6e2c8534203fd6c147451d35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af379ba5a9cf6cab6815c3252ce23beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
(2)已知点A(0,1)、点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c85c66ab0b89e84a10aad864251771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d85d8c1f8add55bdc8c393be3ba2ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0009bbfff99038d2af22c753b87136dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757b384946bb1b4ff9b754ee6aa7f4d3.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70991c59719c9c37e186a7bc8a121ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4401491646ca39b6376c31f1f515b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8f64ebec4a71a609204458cc54df82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
您最近一年使用:0次
2018-12-05更新
|
863次组卷
|
5卷引用:2.1 直线的倾斜角与斜率-2021-2022学年高二数学尖子生同步培优题典(人教A版2019选择性必修第一册)
(已下线)2.1 直线的倾斜角与斜率-2021-2022学年高二数学尖子生同步培优题典(人教A版2019选择性必修第一册)【全国百强校】上海市复旦附中2018-2019学年高二上学期期中考试数学试题上海市上海师范大学附属中学2020-2021学年高二上学期期中数学试题上海市青浦高级中学2020-2021学年高二上学期期中数学试题上海市建平中学2022-2023学年高一下学期期末数学试题