名校
解题方法
1 . 在平面直角坐标系xOy中,若圆
(r>0)上存在点P,且点P关于直线
的对称点Q在圆
上,则r的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a23272c8ee659834fd8014240223fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1485c8ebe275b99df0acf6d91a4230fc.png)
A.(2,+∞) | B.[2,+∞) | C.(2,8) | D.[2,8] |
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2023-11-30更新
|
369次组卷
|
2卷引用:天津市武清区2023-2024学年高二上学期11月期中数学试题
2 . 已知空间向量
则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c519ef15e571106186e0f35a20fbfb92.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 若直线l与直线x+2y=0垂直,且与圆
相切,则l的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8f66edfd714bcc4c499288f0f67e4a.png)
A.x+2y-8=0 | B.x+2y+2=0 | C.2x-y-1=0 | D.2x-y-10=0 |
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4 . 已知直线过点(2, 1),且横截距
、纵截距
满足
,则该直线的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc74a59278eeff35f6124de666b0561.png)
A.2x+y-5=0 | B.x+2y-4=0 |
C.x-2y=0或x+2y-4=0 | D.x-2y=0或2x+y-5=0 |
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5 . 直线
的倾斜角为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d0b13a6875a9fde18f435ba9fe9975.png)
A.45° | B.60° | C.120° | D.150° |
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解题方法
6 . 如图,
且
,
,
且
,
且
,
平面
,
,M是AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/5adf0929-b1c9-462c-9fec-4e576de708e9.png?resizew=161)
(1)若
求证:
平面DMF;
(2)求直线EB与平面DMF所成角的正弦值;
(3)若在DG上存在点P,使得点P到平面DMF的距离为
,求DP的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aabb9d68cfb70f66bb7a52c2e961dd10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc143c7fd7c471ca91b6ccc22438fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6121c4ae264961f49bc9008b0e9ca9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee573ad62dc536a05dadf5008f1afb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755d575f0a87f3345e232b66d5956070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cf187bc2ede965870b90757b495f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b091ee5a8b32424b2b836dde7860c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/5adf0929-b1c9-462c-9fec-4e576de708e9.png?resizew=161)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1029496e181d2aba81bae248d9e05dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f214481e6b23307a37940f6dd0313d30.png)
(2)求直线EB与平面DMF所成角的正弦值;
(3)若在DG上存在点P,使得点P到平面DMF的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc269b2ccd1cc42c7036eaf1ecc519e2.png)
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解题方法
7 . 已知圆C过点A(8,-1),且与直线
相切于点B(3, 4).
(1)求圆C的方程;
(2)过点P(-3,0)的直线
与圆C交于M,N两点, 若
为直角三角形,求
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b172ffec2e6cc2c1cf86a85ba5da8b28.png)
(1)求圆C的方程;
(2)过点P(-3,0)的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037d45b0332e6394e37e517f3a57500c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599fa74fddd8015e645bf701879393b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037d45b0332e6394e37e517f3a57500c.png)
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8 . 如图,在三棱锥
中,PA⊥平面ABC,AB⊥BC,E,F,M分别为AP,AC,PB的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee442383c56eea63a7ab6fa39332010.png)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cdf6198a6b0ad5c3b11d0eb3f660c60.png)
(2)求直线EF与AB所成角的余弦值;
(3)求平面PAC与平面PBC夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2aaed1e9ead175f30f7130569d0411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee442383c56eea63a7ab6fa39332010.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/91473723-3601-4a22-b6fd-3ff5aa6e0624.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cdf6198a6b0ad5c3b11d0eb3f660c60.png)
(2)求直线EF与AB所成角的余弦值;
(3)求平面PAC与平面PBC夹角的大小.
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解题方法
9 . 已知
的三个顶点
,
,
.
(1)求边
所在直线的方程;
(2)求边
上的高所在直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48218f26d084dfb807b5d4eed37c7ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9877e416763059f3a1585d9144ca23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338b0e1dde72defd8069eb7b81c7c9b1.png)
(1)求边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)求边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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10 . 已知点
,
,O为坐标原点,向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2e5010f5b983c9c0b30bb4ebdc9fff.png)
(1)求向量
的单位向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc82ca663a64bb807b74e1eaa59e842.png)
(2)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42af2f16b30003e2cd42b42d21732c4.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97130ba1c0ba45f6d15e66aa1646ee2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b37762afb7ef73aea60210818911287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2e5010f5b983c9c0b30bb4ebdc9fff.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc82ca663a64bb807b74e1eaa59e842.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42af2f16b30003e2cd42b42d21732c4.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e0f64271754d751c2de87abbdfd803.png)
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