解题方法
1 . 已知点
,过点P向直线
:
和
:
作垂线,垂足分别为点M,N,则线段MN的长是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f40d5459e1385ab7d829ea96ca0b946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d532ce76942846df88c6f66112e50f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 甲、乙两队各有
个队员,已知甲队的每个队员分别与乙队的每个队员各握手一次(同队的队员之间不握手),从这
次握手中任意取两次.记事件
:两次握手中恰好有4个队员参与;事件
:两次握手中恰好有3个队员参与.
(1)当
时,求事件
发生的概率
;
(2)若事件
发生的概率
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
(2)若事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1ae55cda6e1176109352d7bde95921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
3 .
、
是已知圆
的两条互相垂直的半径,延长
至点P,延长
至点Q.使得
,
.
(1)若直线OP和OQ的斜率都存在,试确定直线OP和OQ的斜率的乘积是否为一个常数?
(2)试确定
是否为一个常数?
(3)设
.试确定是否存在两个定点
、
,使
,
的斜率的乘积为一个常数?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88ec2dbad3fa6208c0493291e5ccdcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f304a24bb2e199772c53223db7b4be9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88ec2dbad3fa6208c0493291e5ccdcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f304a24bb2e199772c53223db7b4be9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d388a3e54d3a0a19d064fc7ca00459b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799a839722766253265f9da8d582982b.png)
(1)若直线OP和OQ的斜率都存在,试确定直线OP和OQ的斜率的乘积是否为一个常数?
(2)试确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc54eca5a663aa7a6bc2273bc05869d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074185b639a471cbc8107e54bac0fe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c2cc110e46ae4b3432814810e28bcf.png)
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4 . 射线OA的方程是
,射线OB的方程是
,长为
的动线段MN的端点M在OA上移动,端点N在OB上移动,则MN的中点
的轨迹方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585ce757983d44bcd0b30fbf8f865f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce02ede96656abd10ee2c8c6554c6fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
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5 . 在直角坐标系xOy上有两点
、
,给定三个条件:①
,②
,③
.请从上述三个条件中选出两个分别填在下列空白处(只填代号),使其构成一个真命题:当且仅当___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3539590ba3e226d4d6480f8460a6247d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f12e628b7b0bd5c387c4c46cef47c17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f52965de7291b547f4c325d3626bd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc261508f42e75323971f0b8282b0ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e8c4db99a1f1ef1032002a070d65a0.png)
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解题方法
6 . 直角三角形的两直角边长分别为
,斜边长为
,其内切圆与外接圆的半径分别为
,当
变化时,试求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dce64d610e7f309e414d9abe7ff2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be7318e38fcc8ad1b40f448ed7b9703b.png)
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7 . 已知正整数n满足条件:存在唯一的整数k,使
成立.这样的n的最大值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf338de7f21f662a32145d4516b77a54.png)
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解题方法
8 . 从编号分别为1,2,…,9的9张卡片中任意抽取3张,将它们的编号从小到大依次记为
,则
且
的概率是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5768313a382ee3d30dee807592ac36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3da0d45770a8c3bb4965872321dcce6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 已知
,若方程
的根
和
满足
.
(1)在平面直角坐标系
中,画出点
所表示的区域,并说明理由;
(2)令
,求
的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2b59e7080503a1f7e9d99e7db8fd5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74457dc76d16897775a5021da7e3a3a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9733d0dc09a6c9f7db3543ddb3f007b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/7b30e585-d1aa-4ea6-894c-834eb8cf45c7.png?resizew=168)
(1)在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb6f70c26a40ac89ae3095b03dd2ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63313f7ac7402fcb5a9a840db64c6f08.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8f9a46150968652a080d12b316f543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
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解题方法
10 . 如图的实验装置是由两块互相垂直的正方形木板构成的.已知两个正方形的边长都为
,在正方形
的对角线
上有一滑片
,在正方形
的对角线
上有一滑片
,无论两个滑片如何滑动,始终满足滑片
到点
的距离等于滑片
到点
的距离.则四面体
体积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25e3444b32197148084b75af530817c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/20/ea31664a-1973-491c-942b-4bf7e5328853.png?resizew=167)
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