名校
1 . 如图,在三棱锥
中,
,其中
分别是
的中点.
平面
;
(2)求点
到平面
的距离;
(3)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/adff2d8120ddf9cac95772463f479bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbaa7e5dd051ff18e06f1fef16494b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fb86bc134ac6560644fda0f9f05c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2273ae1ee99cec9c1304323bc9ebf75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
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名校
2 . 已知抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
(
)的焦点为
,准线为
,点
在抛物线
上,点
在准线
上,若
是边长为6的等边三角形,则
的值是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4139b091e9dc432b267ff68420c77de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
A.3 | B.![]() | C.6 | D.![]() |
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名校
解题方法
3 . 已知椭圆C:
的右焦点为
,右顶点为A,直线l:
与x轴交于点M,且
,
(1)求C的方程;
(2)B为l上的动点,过B作C的两条切线,分别交y轴于点P,Q,
①证明:直线BP,BF,BQ的斜率成等差数列;
②⊙N经过B,P,Q三点,是否存在点B,使得,
?若存在,求
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eecbc96a8c7c9fa3c8c175931731b2.png)
(1)求C的方程;
(2)B为l上的动点,过B作C的两条切线,分别交y轴于点P,Q,
①证明:直线BP,BF,BQ的斜率成等差数列;
②⊙N经过B,P,Q三点,是否存在点B,使得,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d484860d9392ecacc942edecd37b6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c2f99ac2b6bc91b983628b68a5cd0d.png)
您最近一年使用:0次
2024-03-22更新
|
2345次组卷
|
5卷引用:安徽省芜湖市安徽师范大学附属中学2023-2024学年高二下学期4月期中考试数学试题
名校
4 . 如图,在四棱锥
中,四边形ABCD是正方形,PA⊥平面ABCD,
,点E,F分别为棱PB,BC的中点.
;
(2)求平面AEF与平面ECD所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4486d52b6e410fd7b60428121d96cef.png)
(2)求平面AEF与平面ECD所成二面角的正弦值.
您最近一年使用:0次
2024-03-08更新
|
877次组卷
|
3卷引用:安徽省芜湖市安徽师范大学附属中学2023-2024学年高二下学期4月期中考试数学试题
5 . 命题“
”的否定是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a44156b1dc9950951ddae8fb34456b8.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6 . 已知椭圆
的上、下顶点分别为M,N,点P为椭圆上任意一点(不同于M,N),若点Q满足
,则点Q到坐标原点距离的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7e3ead1577781db7cb4f072c42a03f.png)
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2024-02-17更新
|
409次组卷
|
2卷引用:安徽省芜湖市2023-2024学年高二上学期1月期末教学质量监控数学试题
7 . 如图,在三棱柱
中,M,N分别是线段
上的点,且
.设
,且均为单位向量,若
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2743e10dd8bce468d1d397b3e9a550d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7858eaa13d53592a6fdc63d7de28057b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c01e7c22a736cba039fc4b2913e185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17df623122e2cfefe652b417cc436506.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/7c923bc0-1a2b-4e39-a06d-7231ce106b9a.png?resizew=160)
A.![]() ![]() ![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
8 . 已知椭圆
的左顶点和右焦点分别为A,F,点P为椭圆外一点,线段PA,PF恰好均被椭圆平分,且与椭圆分别交于M,N两点,当
时,椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2539599cde39d8bff3f254c42c193fd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 如图,在四棱锥
中,底面ABCD是矩形,
平面ABCD,
.若点O,M分别为棱AC,PD的中点,点N在棱PC上,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/a4082fc0-b3de-4a54-bb1e-7633edc5d706.png?resizew=180)
(1)求线段MN的长;
(2)求平面ACM与平面BON夹角的余弦值.
![](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/d8762fff0ad4125ed891fd278ec76e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ee42d7d94bc89c0ee62c61b475b6eb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/a4082fc0-b3de-4a54-bb1e-7633edc5d706.png?resizew=180)
(1)求线段MN的长;
(2)求平面ACM与平面BON夹角的余弦值.
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解题方法
10 . 在平面直角坐标系
中,已知双曲线
的左、右焦点分别为
,焦距为4,右顶点到点
的距离之差为
.
(1)求双曲线的标准方程;
(2)点P在双曲线C上,且射线
分别交双曲线于点M,N,求直线MN斜率k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db0cc24753f6ea44c19c3cc49e26024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f98254a6193566587a70c7d95fdabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f98254a6193566587a70c7d95fdabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求双曲线的标准方程;
(2)点P在双曲线C上,且射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74c5df422b0b7b0736baf83ba3b00d2.png)
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