名校
1 . 如图,在三棱锥P-ABC中,
底面ABC,
,
,E为PC的中点,点F在PA上,且
.
平面PAC;
(2)求平面ABC与平面BEF所成的二面角的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3cc9cccfb4c260dac05f4ed57e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97aa0d985b33b0d82571b0b3a383e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216b9a949b87bd815f5937501a3c97ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
(2)求平面ABC与平面BEF所成的二面角的平面角的余弦值.
您最近一年使用:0次
名校
2 . 如图,在三棱柱
中,
.
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca079262781ff681048d99ea02c2bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd38f4fd6af2418573bcc7b67119be5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf1cc9995c3846117daa8cf10aadf22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
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名校
解题方法
3 . 已知抛物线C:
,O为坐标原点,F为抛物线C的焦点,点A,B为抛物线上两点,且满足
,过原点O作
交AB于点D,若点D的坐标为
,则抛物线C的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cee097d4fe948c3d4f1b5c28b24adf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.png)
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解题方法
4 . 在直角坐标平面内,已知点
,动点
.设
、
的斜率分别为
,且
.设动点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
的直线
交曲线
于
两点,是否存在常数
,使
恒成立?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafdf8b4a9210f9cb02756294a395a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712a4253fe8b45eee457c5112d546f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcb71b9faccca05307b72582a3be8cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcf02e64b9374c513c6bf9c31ad3cf0.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/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f6545388fa17b4e0d1d2013b58db82.png)
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解题方法
5 . 已知椭圆
:
经过
,
,
,
,
这5个点中的4个点.
(1)求
的方程.
(2)设直线
与
交于不同的两点
,
.
①证明:存在常数
,使得
为定值.
②若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2085af2326d0e13a12d3db8dbb79f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d38c670ff6957144c4a8d2550065c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7328c4b1805eaa091bc43e02b28cc93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135438dd8cd5191a6daa59b3a275b3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5678056e8a55010125877dce0f3a8363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d598c40eade0d9aba767398c8919e0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d0aafd52e26c241c46d0206f42f415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
①证明:存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87c9d0b21a7f6f45c146cedcfec1553.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e35c6c8effa387df4970e1d332b3ea3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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6 . 如图,在长方体
中,E,F分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/11/3cda7224-1b73-41a3-b965-1df205a16ec5.png?resizew=154)
(1)证明:
平面
.
(2)若
,
,长方体
外接球的表面积为
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/11/3cda7224-1b73-41a3-b965-1df205a16ec5.png?resizew=154)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8197bf06d017950c85c3ba6a291c095e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b363d15cf5e43c963b4d16ea1b8bec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
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解题方法
7 . 如图,在四棱锥
中,底面
为直角梯形,
,
平面
,
,点
分别在线段
和
的中点.
平面
;
(2)求平面
与平面
夹角.
![](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/405effb49ef901476701e72cc47918da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95475bfc06e884754eb4a455c3f434e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd706c0e3aa382425502a1262dc6b735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c7c261740ac2ae26715e1298ca278a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5f236e0c248607721ff77b6ea8b6ee.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5f236e0c248607721ff77b6ea8b6ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b81fb655624ff75a5eab94de9b8c8e9.png)
您最近一年使用:0次
2024-06-08更新
|
328次组卷
|
2卷引用:云南省玉溪市红塔区云南省玉溪第一中学2023-2024学年高二下学期6月月考数学试题
名校
解题方法
8 . 设F为抛物线
的焦点,A,B,C为抛物线上三点,若F为
的重心,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26ec5998ca8591bacd694d2fbf3b42c.png)
A.6 | B.8 | C.10 | D.12 |
您最近一年使用:0次
2024-06-08更新
|
538次组卷
|
2卷引用:云南省玉溪市红塔区云南省玉溪第一中学2023-2024学年高二下学期6月月考数学试题
名校
解题方法
9 . 下列结论正确的是( )
A.直线![]() ![]() ![]() |
B.已知直线![]() ![]() ![]() |
C.已知直线![]() ![]() ![]() |
D.已知直线l过定点![]() ![]() ![]() |
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10 . 已知双曲线
的右焦点为
,左、右顶点分别为
轴于点
,且
.当
最大时,点
恰好在
上,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d9b8ec00bea3d46369592a473f720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626e4e5bf9f6d13ebcdfaa4dffe8dcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7d6bb0efbf3e05cc4f7f232b90f139.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/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.2 | D.![]() |
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