名校
解题方法
1 . 如图1,某十字路口的花圃中央有一个底面半径为2
的圆柱形花柱,四周斑马线的内侧连线构成边长为20
的正方形.因工程需要,测量员将使用仪器沿斑马线的内侧进行测量,其中仪器P的移动速度为1.5
,仪器的移动速度为1
.若仪器Р与仪器Q的对视光线被花柱阻挡,则称仪器Q在仪器P的“盲区”中.
![](https://img.xkw.com/dksih/QBM/2021/11/6/2845466838155264/2847719718584320/STEM/024c5be3-060b-4485-8035-74e62f6089a8.png?resizew=538)
(1)如图2,斑马线的内侧连线构成正方形ABCD,仪器Р在点A处,仪器Q在BC上距离C点4
处,试判断仪器Q是否在仪器P的“盲区”中,并说明理由;
(2)如图3,斑马线的内侧连线构成正方形ABCD,仪器P从点A出发向点D移动,同时仪器Q从点C出发向点B移动,在这个移动过程中,仪器Q在仪器Р的“盲区”中的时长为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22964de2a093c97a8755dbe70487735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22964de2a093c97a8755dbe70487735e.png)
![](https://img.xkw.com/dksih/QBM/2021/11/6/2845466838155264/2847719718584320/STEM/024c5be3-060b-4485-8035-74e62f6089a8.png?resizew=538)
(1)如图2,斑马线的内侧连线构成正方形ABCD,仪器Р在点A处,仪器Q在BC上距离C点4
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
(2)如图3,斑马线的内侧连线构成正方形ABCD,仪器P从点A出发向点D移动,同时仪器Q从点C出发向点B移动,在这个移动过程中,仪器Q在仪器Р的“盲区”中的时长为多少?
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2021-11-09更新
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1244次组卷
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6卷引用:2020届江苏省高三高考全真模拟(八)数学试题
2020届江苏省高三高考全真模拟(八)数学试题(已下线)专题17 实际应用问题-2020年高考数学母题题源解密(江苏专版)江苏省常州高级中学2023-2024学年高二上学期10月阶段检测数学试题广东省深圳市人大附中深圳学校2021-2022学年高二上学期期中数学试题(已下线)专题8 第1讲 直线与圆2.5 直线与圆、圆与圆的位置关系
名校
2 . 如图,设点
为椭圆
的右焦点,圆
过
且斜率为
的直线
交圆
于
两点,交椭圆
于点
两点,已知当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc77638c9a5f1e669225af3344a7966.png)
![](https://img.xkw.com/dksih/QBM/2018/12/10/2093677814841344/2094565759918080/STEM/1ab20f55c0304b2cbaa4eee3d45b6666.png?resizew=176)
(1)求椭圆
的方程.
(2)当
时,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ff150be64d09c7cd4a250113edaeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893d4e8d70ea2c716ac7b6c1777a77f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9173b446b8ff3ec5506540f277d93a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc77638c9a5f1e669225af3344a7966.png)
![](https://img.xkw.com/dksih/QBM/2018/12/10/2093677814841344/2094565759918080/STEM/1ab20f55c0304b2cbaa4eee3d45b6666.png?resizew=176)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb309d0cc58b857b369d10bb6dae01d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ab2337ce84f6840194f67188285491.png)
您最近一年使用:0次
2018-12-07更新
|
1037次组卷
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3卷引用:【全国百强校】江苏省清江中学2019届高三第二次教学质量调研数学试题
3 . 【江苏省苏锡常镇四市2017-2018学年度高三教学情况调研(二)数学试题】如图,椭圆
的离心率为
,焦点到相应准线的距离为1,点
分别为椭圆的左顶点、右顶点和上顶点,过点
的直线
交椭圆于点
,交
轴于点
,直线
与直线
交于点
.
![](https://img.xkw.com/dksih/QBM/2018/7/25/1996163991904256/1997388793798656/STEM/f800325b8454471fb6d7b7278d7ba197.png?resizew=260)
(1)求椭圆的标准方程;
(2)若
,求直线
的方程;
(3)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c38805c09dcfbcc42103308975a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b378a2df371f5ff1815c03a84f571229.png)
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e04b713af80edc1be811c83e6c4fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345632b25ab00040c8930d20e20b9ad2.png)
![](https://img.xkw.com/dksih/QBM/2018/7/25/1996163991904256/1997388793798656/STEM/f800325b8454471fb6d7b7278d7ba197.png?resizew=260)
(1)求椭圆的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7806f1efe16b5e00b41ea74f7be1da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c60bb69220eb1f216bffa96dff09355.png)
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解题方法
4 . 已知椭圆
的方程:
,右准线
方程为
,右焦点
为椭圆的左顶点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/80ad5c02-f5e4-491b-95d5-fb79cc1151f4.png?resizew=206)
(1)求椭圆
的方程;
(2)设点
为椭圆在
轴上方一点,点
在右准线上且满足
且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ee6969d1dba8a4c34e2a2b49cdc642.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/80ad5c02-f5e4-491b-95d5-fb79cc1151f4.png?resizew=206)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc51d69d5d751f11f8158ea43b1f0abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93872dcaa61a80126f63b49f915958e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
您最近一年使用:0次
2018-03-06更新
|
831次组卷
|
2卷引用:江苏省南京师范大学附属中学、天一、海门、淮阴四校2018届高三联考数学调研测试试题
5 . 已知点
,
分别为线段
上的动点,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
(1)若
求直线
的方程;
(2)证明:
的外接圆恒过定点(异于原点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e91aee78b2293d162e117a7a15655a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c483745c2455e26d7e695f5727600ee8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a090d241903d3f409644768e5127568e.png)
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2016-12-03更新
|
1040次组卷
|
8卷引用:2015届江苏省连云港、徐州、淮安、宿迁四市高三一模考试理科数学试卷
2011·江苏南京·一模
解题方法
6 . 在直角坐标系
中,直线
与
轴正半轴和
轴正半轴分别相交于
两点,
的内切圆为圆
.
(1)如果圆
的半径为1,
与圆
切于点
,求直线
的方程;
(2)如果圆
的半径为1,证明:当
的面积、周长最小时,此时
为同一个三角形;
(3)如果
的方程为
,
为圆
上任一点,求
的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)如果圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/0f119f6a7eabd36fca6ef25135311e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)如果圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502bea604848f203c3c6e33bb14318d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e0a0ceab1e6b30513ab7d0b5c376da.png)
您最近一年使用:0次