1 . 如图,正方体
的棱
,
,
,
所在的直线中,与直线
成异面直线的是( )
![](https://img.xkw.com/dksih/QBM/2020/11/10/2590155875131392/2590586443726848/STEM/8fde038067144e2186bca13ad1b2f982.png?resizew=166)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/2020/11/10/2590155875131392/2590586443726848/STEM/8fde038067144e2186bca13ad1b2f982.png?resizew=166)
A.直线![]() | B.直线![]() | C.直线![]() | D.直线![]() |
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北京市第一次普通高中2019-2020学年高二学业水平考试合格性考试数学试题(已下线)8.3 空间点、直线、平面之间的位置关系-2020-2021高中数学新教材配套提升训练(人教A版必修第二册)(已下线)专题8.3 空间点、直线、平面之间的位置关系(B卷提升篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教A版,浙江专用)广西钦州市第四中学2022-2023学年高二上学期第二次学考模拟考试数学试题河北专版 学业水平测试 专题九 立体几何初步河北省秦皇岛市昌黎文汇学校2022-2023学年高一下学期期末数学试题
2 . 已知圆
的圆心坐标为
,且与
轴相切,直线
与圆
交于
,
两点,求
.
某同学的解答过程如下:
解答:因为圆
的圆心坐标为
,且与
轴相切,
![](https://img.xkw.com/dksih/QBM/2020/11/10/2590155875131392/2590586444038144/STEM/ed2960384d0b4604aa602a691f6a1603.png?resizew=189)
所以圆
的半径是2.
所以圆
的方程是
.
因为直线
与圆
交于
,
两点,
联立方程组![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6575a9892a1acad2b25ab59f1216283.png)
解得
或![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c04c8925ff2beebd4c4c3e21de45ca.png)
不妨设
,
,
所以![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c7079d876beb9b855f97e4acf84981.png)
(1)指出上述解答过程中的错误之处;
(2)写出正确的解答过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ee3dd9e294e3e66e60cab20b5f82bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c64fe18cf7bb6e26eb1e4409b441965b.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/084cf5ffced059f5653ee2a1023518b7.png)
某同学的解答过程如下:
解答:因为圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/2020/11/10/2590155875131392/2590586444038144/STEM/ed2960384d0b4604aa602a691f6a1603.png?resizew=189)
所以圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
所以圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550d183b05000722c74baf25eb4a6741.png)
因为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c64fe18cf7bb6e26eb1e4409b441965b.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)
联立方程组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6575a9892a1acad2b25ab59f1216283.png)
解得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6befb747343cf8af3b416ac7a3490bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c04c8925ff2beebd4c4c3e21de45ca.png)
不妨设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6114ce586d4468f1b83c85bf029ba625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc0a380346facb3209baefcb66b1aa4.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c7079d876beb9b855f97e4acf84981.png)
(1)指出上述解答过程中的错误之处;
(2)写出正确的解答过程.
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3 . 已知两条直线
,
和平面
,那么下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() |
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4 . 经过点
,且斜率为2的直线的方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 已知直线
经过
,
两点,那么直线
的倾斜角的大小是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.30° | B.45° | C.60° | D.90° |
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北京市第一次普通高中2019-2020学年高二学业水平考试合格性考试数学试题(已下线)专题9.1 直线与直线方程(精讲)-2021年新高考数学一轮复习学与练四川省眉山市第一中学2020-2021学年高二上学期12月月考理科数学试题江西省宜春市奉新县第一中学2021-2022学年高二上学期第三次月考数学(文)试题苏教版(2019) 选修第一册 一蹴而就 第1章 单元整合
6 . 圆
与圆
的公共点的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e318cefab1d71238b6a770e9d5fe154e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e383fcc122f267043fbafe0972bfb900.png)
A.0 | B.1 | C.2 | D.3 |
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7 . 如图放置的等腰直角
薄片(
,
)沿
轴滚动,点
的运动轨迹曲线与
轴有交点,则在两个相邻交点间点
的轨迹曲线与
轴围成图形面积为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/250c7e3c-bfa9-4a38-a70b-23061707070f.png?resizew=157)
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8 . 有一个六个面分别标上数字1、2、3、4、5、6的正方体,甲、乙、丙三位同学从不同的角度观察的结果如图所示.如果记2的对面的数字为
,3的对面的数字为
,则方程
的解
满足
,
为整数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466bcd13574f99c7113dc86102a94d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cce2c1be9c5058782d06ba0427f2cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/937cff74-785e-490d-9377-4eeebb794d56.png?resizew=248)
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9 . 已知圆
圆心为坐标原点,半径为
,直线
:
交
轴负半轴于
点,交
轴正半轴于
点
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/ab5730c4-d31a-4978-952c-21706fd99f47.png?resizew=436)
(1)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a457b899731577bfe61dda594ae4eec4.png)
(2)设圆
与
轴的两交点是
,
,若从
发出的光线经
上的点
反射后过点
,求光线从
射出经反射到
经过的路程
(3)点
是
轴负半轴上一点,从点
发出的光线经
反射后与圆
相切.若光线从射出经反射到相切经过的路程最短,求点
的坐标
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6df6af9a2a8137eb00236e28441848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/ab5730c4-d31a-4978-952c-21706fd99f47.png?resizew=436)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a457b899731577bfe61dda594ae4eec4.png)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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10 . 如图,三棱柱
中,底面
,
,三个侧面都是矩形,
,
为线段
上的一动点,则当
最小时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7277d4fa62666459e91b0f16f3756c65.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39417d678f2db936ca1dc42b7d6a08c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7277d4fa62666459e91b0f16f3756c65.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/997d26f9-e09a-495b-a06a-7799110dc269.png?resizew=164)
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