1 . 如图,在矩形ABCD中,
,
,沿BD将△ABD折起至
的位置.若点
在平面BCD上的射影落在△BCD的内部(包含边界),则四面体
体积的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea25ef38e4afa8f75ffd0842890289.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc84671fd0f27587260cdbcc31e6d483.png)
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2 . 阿波罗尼斯是古希腊著名数学家,与阿基米德、欧几里得并称为亚历山大时期数学三巨匠,他研究发现:如果一个动点
到两个定点的距离之比为常数
(
,且
),那么点
的轨迹为圆,这就是著名的阿波罗尼斯圆.若点
到
,
的距离比为
,则点
到直线
:
的距离的最大值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76218cf7a5779168198df12edafa276a.png)
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2024-06-11更新
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3 . 若曲线
与直线
有两个交点,则实数k的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c6b82a8b5fb6deb81d13f477e2cb3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bd95c6cda85d00e5a5b53d2e9af5eb.png)
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4 . 已知直线
和圆
交于
,
两点,
为坐标原点,若
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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5 . 圆
:
关于直线
:
对称的圆的标准方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea829372272eb77138449465484c0ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baabfd32465e9e50409413d9c1358279.png)
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2023-11-18更新
|
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6 . 已知直线
:
,圆
:
,则下列命题:①圆
截直线
的最短弦长为4;②圆
上一定存在4个点到直线
的距离为
;③直线
与圆
交于
,
两点,则
面积的最大值为4;④直线
与线段
相交,其中
,
,则
的取值范围是
.其中正确的是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1111fea5c47ce1fdfc9ec28ac370955.png)
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7 . 已知实数
,
满足方程
,当
时,
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1576770308cd3a340859c462b557ed9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e546d27d099d383c2abff1f46139824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9300f28826e59e333e042a562e837b74.png)
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8 . 直线
,若直线分别与x轴,y轴的负半轴交于A、B两点,求三角形AOB面积的最小时的直线的方程______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cadd4cfce20dc27aa13c67afe46d2ddc.png)
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2023-10-24更新
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内蒙古乌兰察布市四子王旗宽高实验学校2023-2024学年高二上学期期中数学试题河北省河北师范大学附属中学2023-2024学年高二上学期10月月考数学试题(已下线)高二数学上学期期中模拟卷01(原卷版)
9 . 过圆
外一直线
上一动点P作圆的切线,则切线长最小值为_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e383fcc122f267043fbafe0972bfb900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f61de965b9d38982e5a75af2737e57.png)
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名校
解题方法
10 . 已知圆
,直线
.当直线l被圆C截得弦长取得最小值时,直线l的方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364757018222df5069a83bff7ac93c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48130ad44f005dc3821006663695542a.png)
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