名校
解题方法
1 . 三等分角是古希腊几何尺规作图的三大问题之一,如今数学上已经证明三等分任意角是尺规作图不可能问题,如果不局限于尺规,三等分任意角是可能的.下面是数学家帕普斯给出的一种三等分角的方法:已知角
的顶点为
,在
的两边上截取
,连接
,在线段
上取一点
,使得
,记
的中点为
,以
为中心,
为顶点作离心率为2的双曲线
,以
为圆心,
为半径作圆,与双曲线
左支交于点
(射线
在
内部),则
.在上述作法中,以
为原点,直线
为
轴建立如图所示的平面直角坐标系,若
,点
在
轴的上方.
的方程;
(2)若过点
且与
轴垂直的直线交
轴于点
,点
到直线
的距离为
.
证明:①
为定值;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a998a7d4d980e848ee050b706480ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e587c886cd9f7d48f0cce82dcb940c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75eb52879657138c23304b1634c73f7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.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/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d566a90ab70e7133f0f110143a4f06ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5881b1640911274127b9aa3d647ee903.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/ac047e91852b91af639feec23a9598b2.png)
(2)若过点
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
证明:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422fd5f0bdef76f7f05c6f803dddc982.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d566a90ab70e7133f0f110143a4f06ae.png)
您最近一年使用:0次
解题方法
2 . 双曲线C:
的左、右焦点分别为
、
,过
且倾斜角为
的直线为
,过
且倾斜角为
的直线为
,已知
,
之间的距离为
.
(1)求C的方程;
(2)若过点
的直线l与C的左、右两支分别交于
两点(点
不在x轴上),判断是否存在实数k使得
.若存在,求出k的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247c5b95745e280f039f8daa90ddecb6.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/d387d228f512ada68fc79c9d5775b077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d387d228f512ada68fc79c9d5775b077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
(1)求C的方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad57e3727b7bbd795b05332fbf9649e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad57e3727b7bbd795b05332fbf9649e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb71288fd1d0585d76040f828ea5595.png)
您最近一年使用:0次
名校
解题方法
3 . “曼哈顿距离”是人脸识别中一种重要的测距方式.其定义为:如果在平面直角坐标系中,点
的坐标分别为
,那么称
为
两点间的曼哈顿距离.
(1)已知点
分别在直线
上,点
与点
的曼哈顿距离分别为
,求
和
的最小值;
(2)已知点
是曲线
上的动点,其中
,点
与点
的曼哈顿距离
记为
,求
的最大值.参考数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6037359d2727b05ee33db9e2c36226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093c6d5bcaa69cea79b24688f5d1bd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c37a37e91dd29058e66d8d905e5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00535516e08775f69df930f449f4469e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ce60648ea5042ab5eb5702efe651a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c37a37e91dd29058e66d8d905e5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77e22dd917201d812897e3b4d1c52ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edc218828907b5918bf9d755eb98ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a9be71b631f37d8a88bc7bd030aa79.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e18b23c806c5c76de3244b015911e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d25e70d37af93796965efc8d342185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad135b14c9dcd83eab6618d7694c7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f513553d63e9c87a70dd6aa57f97b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c33d08de0e3d2643654f22543132491.png)
您最近一年使用:0次
解题方法
4 . 已知抛物线
的焦点为
.点
在抛物线
上,且
.
(1)求
;
(2)过焦点
的直线
交抛物线
于
两点,原点为
,若直线
分别交直线
:
于
两点,求线段
长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f44db0e2c2cf4da32aaccb5683c8caf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c438531a5c9508d14ef7008eb4e732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c9aa5dc8e688868ad3eac88714cd51.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)过焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abfdd1e8e9a16c04d58ee0cc3382192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
5 . 已知
是圆
上的动点,
为定点,线段
的垂直平分线交线段
于点
,点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
的动直线
交曲线
于不同的A,B两点,
为线段
上一点,满足
,证明:点
在某定直线上,并求出该定直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd90fb00c0ffeaed8b9448e3a043f2c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b707fdf035eb2fb4467958893c60381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ba9d9535a1d7e34f66db9da0861394.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3f2e9c21be0d3b6dea179d01fab006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
名校
解题方法
6 . 双曲线
的离心率为
,圆
与
轴正半轴交于点
,点
在双曲线
上.
(1)求双曲线
的方程;
(2)过点
作圆
的切线交双曲线
于两点
、
,试求
的长度;
(3)设圆
上任意一点
处的切线交双曲线
于两点
、
,试判断
是否为定值?若为定值,求出该定值;若不是定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.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/46529ee9b4550db1c12f187e1fbebde0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/411461db15ee8086332c531e086c40c7.png)
(3)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/79188647c574441c2414c3781a0ef543.png)
您最近一年使用:0次
2023-11-24更新
|
1029次组卷
|
5卷引用:专题03 圆锥曲线方程(3)
(已下线)专题03 圆锥曲线方程(3)(已下线)重难点7-2 圆锥曲线综合应用(7题型+满分技巧+限时检测)(已下线)专题07 解析几何(三大类型题综合)15区新题速递上海市向明中学2023-2024学年高二下学期期中考试数学试题上海市进才中学2023-2024学年高三上学期期中考试数学试卷
7 . 已知点
是圆
:
上一动点(
为圆心),点
的坐标为
,线段
的垂直平分线交线段
于点
,动点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)
,
是曲线
上的两个动点,
为坐标原点,直线
、
的斜率分别为
和
,且
,则
的面积是否为定值,若是,求出这个定值;若不是,请说明理由;
(3)设
为曲线
上任意一点,延长
至
,使
,点
的轨迹为曲线
,过点
的直线
交曲线
于
、
两点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bc00148729558bbe435bad010c93fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375bad9fb4833dafb6499a518867bbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b6891348ca27c53f5e732d6187ee12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
(3)设
![](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/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56b32ddc6969b161fa2a1b3ae73d33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](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/8b17f20c25bb16153b5f2d25062ed7a7.png)
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4卷引用:2.5 曲线与方程(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
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8 . 在平面直角坐标系xOy中,定义
,
两点间的“直角距离”为
.
(1)填空:(直接写出结论)
①若
, 则
;
②到坐标原点的“直角距离”等于1的动点的轨迹方程是 ;
③记到M(-1,0),N(1,0)两点的“直角距离”之和为4的动点的轨迹为曲线G,则曲线G所围成的封闭图形的面积的值为 ;
(2)设点A(1,0), 点B是直线
上的动点,求ρ(A,B)的最小值及取得最小值时点B的坐标;
(3)对平面上给定的两个不同的点
,
,是否存在点C(x,y), 同时满足下列两个条件:
①
;
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2466d223bbf22896a350f2c46eee3c5.png)
若存在,求出所有符合条件的点的集合;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a97b49a5539ea7c791da1beb0a83c49.png)
(1)填空:(直接写出结论)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca1d2645ca6fd82a0483e6bc962eb14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daca6e9e7f98d284cadef013e413ca23.png)
②到坐标原点的“直角距离”等于1的动点的轨迹方程是 ;
③记到M(-1,0),N(1,0)两点的“直角距离”之和为4的动点的轨迹为曲线G,则曲线G所围成的封闭图形的面积的值为 ;
(2)设点A(1,0), 点B是直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4349a46e3c054b326644f2aafd312536.png)
(3)对平面上给定的两个不同的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9361963efd6a9027e8dc91edf9aa7b8b.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2466d223bbf22896a350f2c46eee3c5.png)
若存在,求出所有符合条件的点的集合;若不存在,请说明理由.
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6卷引用:2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19
(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19(已下线)专题02 直线和圆的方程(5)(已下线)第1章 坐标平面上的直线 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)1.4点到直线的距离(十八大题型)(3)湖北省部分学校2024届高三下学期模拟考试数学试题北京市昌平区第一中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
9 . 最近国际局势波云诡谲,我国在某地区进行军事演练,如图,
是三个军事基地,
为一个军事要塞,在线段
上.已知
,
,
到
,
的距离分别为5km,
.以点
为坐标原点,直线
为
轴,建立平面直角坐标系如图所示,
位于第一象限.
(1)求两个军事基地
的长;
(2)若要塞
正北方向距离要塞10km处有一
处正在进行爆破试验,爆炸波生成
时的半径为
(参数
为大于零的常数),爆炸波开始生成时,一飞行器以
的速度自基地A开往基地
,问参数
控制在什么范围内时,爆炸波不会波及到飞行器的飞行.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f5e21d225bf3c159ddf3876fbb8fb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85b80a20a9d24b13fa776799ede9723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02237a2215fc22f25da4d218b0d0f33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7f45a99cb2a81cfc5a26ed9eddc1ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/25/c36f3b09-2b19-4028-a7e9-07b5d2b8e3b3.png?resizew=176)
(1)求两个军事基地
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若要塞
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ee630252dc9ec9c8453d1561a81743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74ae2d0aa744ab9116e1bfa78564d9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e547ffdf02fd21f3950a1ac4cc2b703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 设
,
是平面直角坐标系xOy上的两点,现定义由点A到点B的一种折线距离
为
.对于平面xOy上给定的不同的两点
,
.
(1)若点
是平面xOy上的点,试证明:
.
(2)在平面xOy上是否存在点
,同时满足:①
;②
?若存在,请求出所有符合条件的点;若不存在,请予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5191ea78656cad7ca36ea6016cc7c7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd1f1df97da3fbbbe23b95b6c6aca6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9a016fd7021b9e9625c8d5f0938ad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/220906577d5afa0c3dd259c88d8b9ced.png)
(2)在平面xOy上是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9a016fd7021b9e9625c8d5f0938ad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893bbe22c8c561d4b5762655db569610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a895dec6f0789295ceb0b6a2f7f431.png)
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