名校
解题方法
1 . 已知平面区域
,记
的面积分别为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237659a75ecb5d2cfddd269dab6c31c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13edbb78a03b29a4f3786de2f900717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
2 . 如图,设
,
是圆O:
上的两个动点,点M关于原点的对称点为
,点M关于x轴的对称点为
,若直线
,
与y轴分别相交于
和
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3fa6438d73fac62ea3d535f1c1cdab.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27663c6e3a3deb55bf1001460fecfd20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566b349adddfbd4144f0ecf7a13b05bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924d2a2d9437355998498de38b5ebf54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2832f82fdeafa819c92ca5c1e74eb5ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5905cfcc5af4b01d63237486eb6d295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3fa6438d73fac62ea3d535f1c1cdab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/17/b64d43cd-4817-43d5-adf9-6bbca4bae6c4.png?resizew=192)
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名校
3 . 已知曲线
的方程为:
有下列四种描述
(1)曲线
关于
对称;
(2)曲线
的面积大于16;
(3)曲线
与圆
有四个公共点;
(4)若
,
为曲线
与
轴的交点,
为曲线
上的点,则
的面积最大为
;则其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2f4e6b75255ad81a871811ebf27266.png)
(1)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d35465f3e40ce00a1dce54b943ae183.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafa8e628e4995e60cc3400028e900b6.png)
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4 . 圆
关于直线
对称的圆的方程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c846a65b4e27fa4f4ebfff96660c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
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5 . 已知圆
的圆心在直线
:
上,并且经过点
和点
.若直线
:
上存在点
,过点
作圆
:的两条切线,切点分别为
,
,且
,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e5eea5f7f98ca8632358b7e49ceb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c229111bc1789d62342e93b180fe492e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb4eb87fd9c474fea913e4b68818abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023·全国·模拟预测
6 . 如图,已知过点
的两条直线分别与圆E:
交于点A,B和点C,D,且A,C在B,D的右侧,
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/259c697d-34c0-4909-9b01-24934fb0782d.png?resizew=169)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b73cbe595a76418351f6675a8cb32c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e171327b811e5b11e8767cd71e8d741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb147633f207280c514f2d28be078dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4f652a7ccb2df18efa879a36c02f83.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/259c697d-34c0-4909-9b01-24934fb0782d.png?resizew=169)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023·全国·模拟预测
7 . 古希腊科学家阿基米德对几何很有研究,下面是他发现的一个定理:设
的外接圆的弧
的中点为
,自点
向
,
中较长的边作垂线,垂足为
,则点
平分折线
的长.如图,点
都在圆
:
上,
轴,且
,点
在第一象限,点
为圆
与
轴正半轴的交点,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4665cc756635abc74f907e364d2f26e9.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d80f2addb9f19c08e39b201b226d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab15f71acf24a48b4ea4efac5f09b718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d35465f3e40ce00a1dce54b943ae183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ea84cba8ccd585ad1da1fd204bc3e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c342a9570ef57ba9da945ce37445fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4665cc756635abc74f907e364d2f26e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/30/24b9fcbd-93d1-46f5-b585-4b79879f8621.png?resizew=159)
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8 . 如图,这是某圆弧形山体隧道的示意图,其中底面AB的长为16米,最大高度CD的长为4米,以C为坐标原点,AB所在的直线为x轴建立直角坐标系.
(1)求该圆弧所在圆的方程;
(2)若某种汽车的宽约为2.5米,高约为1.6米,车辆行驶时两车的间距要求不小于0.5米以保证安全,同时车顶不能与隧道有剐蹭,则该隧道最多可以并排通过多少辆该种汽车?(将汽车看作长方体)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/604de4a6-dccd-43be-b7fc-98cc3d7d5863.png?resizew=206)
(1)求该圆弧所在圆的方程;
(2)若某种汽车的宽约为2.5米,高约为1.6米,车辆行驶时两车的间距要求不小于0.5米以保证安全,同时车顶不能与隧道有剐蹭,则该隧道最多可以并排通过多少辆该种汽车?(将汽车看作长方体)
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2023-11-10更新
|
523次组卷
|
9卷引用:河北省部分高中2023-2024学年高二上学期期中数学试题
名校
9 . 关于曲线
,给出下列四个结论:①曲线
关于原点对称,也关于
轴、
轴对称:②曲线
围成的面积是
;③曲线
上任意一点到原点的距离者不大于
;④曲线
上的点到原点的距离的最小值为1.其中,所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ee901966a632604a588c9e27ff2418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c6e646cd2790a3ac7dec6011089fdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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10 . 直线
与圆
相交所形成的长度为整数的弦的条数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94bd921077b5113ec8367296ad98a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d4c7f4680e267fd112da603beae7b2.png)
A.6 | B.7 | C.8 | D.9 |
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