1 . 坐标平面
上的点
也可表示为
,其中
为
轴非负半轴绕原点
逆时针旋转到与OP重合的旋转角.将点
绕原点
逆时针旋转
后得到点
,这个过程称之为旋转变换.
(1)证明旋转变换公式:
并利用该公式,求点
绕原点
逆时针旋转
后的点
的坐标;
(2)旋转变换建立了平面上的每个点
到
的对应关系.利用旋转变换,可将曲线通过旋转转化为我们熟悉的曲线进行研究.
(i)求将曲线
绕原点
顺时针旋转
后得到的曲线方程,并求该曲线的离心率;
(ii)已知曲线
,点
,直线AB交曲线
于
,
两点,作
的外角平分线交直线AB于点
,求|FM|的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f769907ad11c909d27dd855bf0914592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1029aaebd18d54c2c4d83219ccabc17e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3682b5a7157ec7cf8b265bf0d1025c.png)
(1)证明旋转变换公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623c5066668a603bb3d9a8fe05a9e5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca401344cfe39388623409fed20243b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f8906c9d7ce68defb89848faa531ca.png)
(2)旋转变换建立了平面上的每个点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f8906c9d7ce68defb89848faa531ca.png)
(i)求将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89034582719fefec243548a3b5e5a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
(ii)已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a721040f609e2d77d72b5deba330e58f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecb5caa69f91798f56550bdba335c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/36719f1e764ee0e719b65c49fae84677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2 . 已知椭圆
上有一点P,
分别为左、右焦点,
的面积为S,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cdba94f0901390b90660a3351ed14c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91d277aedc8f6e3d9576afa73b8f20e.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.椭圆C内接矩形的周长范围是![]() |
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2021-03-06更新
|
2659次组卷
|
8卷引用:河北省“五个一名校联盟”2021届高三下学期第二次诊断考试数学试题
河北省“五个一名校联盟”2021届高三下学期第二次诊断考试数学试题江苏省南通市通州区2020-2021学年高三上学期第三次调研考试数学试题(已下线)第十一章 圆锥曲线专练5—椭圆小题最值问题-2022届高三数学一轮复习(已下线)第3章 圆锥曲线与方程 单元综合检测(能力提升)(单元培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)专题09 《圆锥曲线与方程》中的取值范围问题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) (已下线)专题25 圆锥曲线压轴小题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)江苏省南京市南京师大附中2024届高三寒假模拟测试数学试题山东省临沂市费县2024届高三下学期开学考试数学试题
3 . 已知曲线
(
为参数),若
,
是
上关于坐标轴不对称的任意两点,
的垂直平分线交
轴于
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db18903e6c7682a1cba7d8aa12ca6715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddfb522b34cecadfb60ae77ea0496cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 选修4-4: 坐标系与参数方程
在直角坐标系
中,直线
经过点
,其倾斜角为
,以原点
为极点,以
轴非负半轴为极轴,与直角坐标系
取相同的长度单位,建立极坐标系,设曲线
的极坐标方程为
.
(Ⅰ)写出直线
的参数方程,若直线
与曲线
有公共点,求
的取值范围;
(Ⅱ)设
为曲线
上任意一点,求
的取值范围.
在直角坐标系
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/d8d4358f04964fc58d1bbe102fc77463.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/335de97022a74fc49f6aa56d5127015c.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/3386ae0e9c704ec7bc2c94b03c6b4456.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/2e190fbd99cc4025b83db3b1623860fd.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/e6ab23ed247447fe92dce05a7de6c0ef.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/467794cb876d4150bf13fa8a19bf9270.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/d8d4358f04964fc58d1bbe102fc77463.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/2d3e271f096d45c69b952c059d387a3c.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/2f9c65549a1a4f88843297cb33b140f8.png)
(Ⅰ)写出直线
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/335de97022a74fc49f6aa56d5127015c.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/335de97022a74fc49f6aa56d5127015c.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/2d3e271f096d45c69b952c059d387a3c.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/2e190fbd99cc4025b83db3b1623860fd.png)
(Ⅱ)设
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/f4b19e6241ae4793832f61014cf46242.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/2d3e271f096d45c69b952c059d387a3c.png)
![](https://img.xkw.com/dksih/QBM/2016/7/6/1572895900696576/1572895906349056/STEM/348b4e866f814511a924360110a8099e.png)
您最近一年使用:0次
2016-12-04更新
|
2613次组卷
|
2卷引用:2015-2016学年辽宁葫芦岛一中等校高二6月联考理数学卷
5 . 在直角坐标系
中,曲线
的参数方程为![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989996544/STEM/919c8c3955894f8280bb1c50b6cd7239.png)
.若以该直角坐标系的原点
为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为:
(其中
为常数)
(1)若曲线
与曲线
只有一个公共点,求
的取值范围;
(2)当
时,求曲线
上的点与曲线
上点的最小距离
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989996544/STEM/a090857b7f8b4c6a96b343f6d813c7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989996544/STEM/919c8c3955894f8280bb1c50b6cd7239.png)
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989996544/STEM/0776c3e003d24842b04cd573e587e710.png)
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/2016/2/22/1572489983975424/1572489989996544/STEM/7c5120a7cf1347f295d42a4b1ab7fe55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bb3d6c02f08a64f3e73a629ef86504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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6 . 已知点
(
)为平面直角坐标系
中的点,点S为线段AB的中点,当
变化时,点S形成轨迹
.
(1)求S点的轨迹
的方程;
(2)若点M的坐标为
,是否存在直线
交S点的轨迹
于P、Q两点,且使点
为
的垂心?若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcf4e2327d67dc697db8eb92a3b05e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95caf7f3544cb542a8a4d62e3e60b808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e15cf9dc66b5f6ef9613567585e95.png)
(1)求S点的轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e15cf9dc66b5f6ef9613567585e95.png)
(2)若点M的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e15cf9dc66b5f6ef9613567585e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb569a9b7aa076137d16581916dba31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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