名校
解题方法
1 . 如图,在棱长为1的正方体
中,
为平面
内一动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.若![]() ![]() ![]() ![]() |
B.平面![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.对于给定的点![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-04-18更新
|
1685次组卷
|
3卷引用:广东省东莞市东华高级中学、东华松山湖高级中学2023-2024学年高一下学期期中教学质量检查(二)数学试题
解题方法
2 . 已知椭圆
:
(
)的离心率为
,以短轴的两个端点和长轴的两个端点为顶点的菱形周长为
.
(1)求
的方程;
(2)若直线
垂直于
轴,且与
交于
,
(
位于第一象限),
为
轴正半轴上且在
内部的一点,连接
并延长分别交
轴、
于
、
,延长
交
于
,连接
,
为线段
的中点,求直线
的斜率与直线
的斜率之和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588c3822b7812e711b4ad86647b15dc1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
您最近一年使用:0次
解题方法
3 . 椭圆
的长轴长为4,且椭圆C过点
.
(1)求椭圆C的标准方程;
(2)已知A、B为椭圆C的左、右顶点,过右焦点F且斜率不为0的直线交椭圆C于点M、N,直线
与直线
交于点P,记
、
、
的斜率分别为
、
、
,问
是否是定值,如果是,求出该定值,如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1721aa6b62fc4c68cb7161f2658117.png)
(1)求椭圆C的标准方程;
(2)已知A、B为椭圆C的左、右顶点,过右焦点F且斜率不为0的直线交椭圆C于点M、N,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.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/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08835a32badb59fb24aa19f91d3c28a9.png)
您最近一年使用:0次
名校
解题方法
4 . 已知直四棱柱
的底面为正方形,
为直四棱柱内一点,且
,其中
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cef779c4fbc36fda6dd590cce01244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3c482b1fc72806cc615656c13d4c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ddf5cc0ed7aed2ea63e93015fcd0e3e.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
5 . 已知椭圆
过点为
.
(1)求椭圆
的方程;
(2)过点
的直线与椭圆
交于不同的两点
,直线
分别与
轴交于点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d1aa22f13f83698d04c842e70da827.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f40d5459e1385ab7d829ea96ca0b946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2013303974d530fce9a9930938f4c2b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ccc04b26256d82bab992ee408ac7a4.png)
您最近一年使用:0次
名校
解题方法
6 . 已知正方体
的棱长为2,点P在正方形ABCD内运动(含边界),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.存在点P,使得![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-02-17更新
|
1364次组卷
|
4卷引用:广东省东莞市东华高级中学2022-2023学年高二下学期期中考试数学试卷
广东省东莞市东华高级中学2022-2023学年高二下学期期中考试数学试卷河北省唐山市2022-2023学年高二上学期期末数学试题(已下线)模块四 专题1 重组综合练(河北)期末终极研习室(高二人教A版)(已下线)第一章 空间向量与立体几何(压轴题专练,精选20题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)
名校
解题方法
7 . 如下图,正方体
中,M为
上的动点,
平面
,则下面说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/5/12/2977927348215808/2978572935225344/STEM/67e969eb-b7ca-48f3-99b8-4364e0a07e0d.png?resizew=222)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/2022/5/12/2977927348215808/2978572935225344/STEM/67e969eb-b7ca-48f3-99b8-4364e0a07e0d.png?resizew=222)
A.直线AB与平面![]() ![]() |
B.点M与点![]() ![]() |
C.点M为![]() ![]() ![]() |
D.已知N为![]() ![]() ![]() |
您最近一年使用:0次
2022-05-13更新
|
2009次组卷
|
5卷引用:广东省广州市六中2022-2023学年高二上学期期中(线上)数学试题
名校
解题方法
8 . 已知双曲线G的方程
,其左、右焦点分别是
,
,已知点P坐标为
,双曲线G上点
,
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8506adc46d5d5e3aca20a0cf68c97699.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.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/081cd41dab0f2a8f84b0e9f1df4843fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5538ed7012d1bec39dae355c49efdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8f8b7f3cacee3bc378440d230260835.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e2df221cf1da1accdddaee5ccd081c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8506adc46d5d5e3aca20a0cf68c97699.png)
您最近一年使用:0次
2022-04-28更新
|
2740次组卷
|
10卷引用:广东省珠海市第二中学2023-2024学年高二上学期第二次阶段考试数学试题
广东省珠海市第二中学2023-2024学年高二上学期第二次阶段考试数学试题辽宁省葫芦岛市2022届高三第一次模拟考试数学试题(已下线)考点21双曲线-1-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)考点8-3 双曲线及其性质(文理)(已下线)专题10 椭圆、双曲线与抛物线(已下线)专题8-3 圆锥曲线小题综合 (讲+练)-2四川省成都市第十二中学(川大附中)2022-2023学年高三下学期三诊热身考试数学理科试题四川省成都市第十二中学(川大附中)2022-2023学年高三下学期三诊热身考试数学文科试题 (已下线)3.2.2 双曲线的简单的几何性质(重难点突破)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)3.2.1 双曲线及其标准方程(重难点突破)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)
名校
解题方法
9 . 阿波罗尼奥斯在其著作《圆锥曲线论》中提出:过椭圆
上任意一点
的切线方程为
.若已知△ABC内接于椭圆E:
,且坐标原点O为△ABC的重心,过A,B,C分别作椭圆E的切线,切线分别相交于点D,E,F,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4977e4c6a500f429f4d85029b8c75bb2.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc26262f7a1603369462c7c2f2197a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9656735f55e5de465e5667ba578d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4977e4c6a500f429f4d85029b8c75bb2.png)
您最近一年使用:0次
2022-04-07更新
|
2896次组卷
|
9卷引用:广东省阳江市2022-2023学年高二上学期期中数学试题
名校
解题方法
10 . 已知椭圆
,其右焦点为
,点M在圆
上但不在
轴上,过点
作圆的切线交椭圆于
,
两点,当点
在
轴上时,
.
(1)求椭圆
的标准方程;
(2)当点
在圆上运动时,试探究
周长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce176fdfbb44b8459f441a8d805013f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c7e3b6c9b4c7c09f0246a6e05c7e1b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a9bf6bda9363dbef5f6ff4bf6a5edf.png)
您最近一年使用:0次
2022-03-30更新
|
3299次组卷
|
9卷引用:广东省2022届高三一模数学试题
广东省2022届高三一模数学试题广东省广州市番禺区2021-2022学年高二下学期期中数学试题广东省揭阳市揭东区2022-2023学年高二上学期期末数学试题(已下线)专题二十三 椭圆与方程(已下线)必刷卷03 (理)-2022年高考数学考前信息必刷卷(全国乙卷)新疆实验中学2022-2023学年高二上学期期中考试数学试题(已下线)专题38 圆锥曲线中的圆问题-1河北省2022届高考临考信息(预测演练)数学试题(已下线)广东省2022届高三一模数学试题变式题17-22