解题方法
1 . 已知曲线C:
,从曲线C上的任意点
作压缩变换
得到点
.
(1)求点
所在的曲线E的方程;
(2)设过点
的直线
交曲线E于A,B两点,试判断以AB为直径的圆与直线
的位置关系,并写出分析过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204dbf02042c70400b167d2d04fd1a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3682b5a7157ec7cf8b265bf0d1025c.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3682b5a7157ec7cf8b265bf0d1025c.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7422cbdb4ad06d155abb2ccdb25ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
您最近一年使用:0次
名校
解题方法
2 . 斜二测画法是一种常用的工程制图方法,在已知图形中平行于
轴的线段,在直观图画成平行于
轴(由
轴顺时针旋转
得到)的线段,且长度为原来的
,平行于
轴的线段不变.如图,在直角坐标系
中,正方形
的边长为
.定义如下图像变换:
表示“将图形用斜二测画法变形后放回原直角坐标系”;
表示“将图形的横坐标保持不变,纵坐标拉伸为原来的
倍”.
经过两次
变换后所得图形为
,求
的坐标;
(2)在第
次复合变换中,将图形先进行一次
变换,再进行一次
变换,
. 记正方形
进行
次复合变换后所得图形为
.过
作
的垂线,垂足为
,若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31c9ff64b11c29441ffc10c8cc70cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe33c85f43cc3208ae16c2796b9188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bf350a619ef25d8d9b988f3db804e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ee712dfc82e1acc31ef8dcad479a39.png)
(2)在第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31c9ff64b11c29441ffc10c8cc70cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d904903ab8465eb522d2b8cde0fc29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36134f01da0f13b340e82e8835324f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24172ca004ead2629ef8541a709419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bd7d18f67e90a7c37fad4252e43c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8c8bb5b1ee645a5e94c72823b5f295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-05-08更新
|
821次组卷
|
2卷引用:浙江省杭州学军中学2024届高三下学期4月适应性测试数学试题
名校
解题方法
3 . 已知椭圆
,经过仿射变换
,则椭圆变为了圆
,并且变换过程有如下对应关系:①点
变为
;②直线斜率k变为
,对应直线的斜率比不变;③图形面积S变为
,对应图形面积比不变;④点、线、面位置不变(平行直线还是平行直线,相交直线还是相交直线,中点依然是中点,相切依然是相切等).过椭圆
内一点
作一直线与椭圆相交于C两点
,则
的面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513a0d65c80b714d5fec54047babb965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0591e83b82a112dfdfd33d2fc0598fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5810eff0d5ee1b8d40eb1371bcbf3986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1584beab4b00b6b109eab85861d9ce19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a150679a41640f65ddf53b3f696d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9deb20b57fe0b94ca8520b55298d6c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
2023-11-24更新
|
241次组卷
|
4卷引用:湖北省云学名校联盟2023-2024学年高二上学期期中联考数学试题
湖北省云学名校联盟2023-2024学年高二上学期期中联考数学试题山东省新泰市第一中学东校2023-2024学年高二上学期第二次质量检测数学试题山东省新泰市第一中学东校2023-2024学年高二上学期第二次月考数学试题(已下线)第28题 通性通法为根基,设参变换有妙招(优质好题一题多解)
名校
4 . 以下命题正确的个数是( )
①在回归直线方程
中,当解释变量
每增加1个单位时,预报变量
平均增加2个单位;
②残差平方和越小的模型,拟合的效果越好;
③散点图中所有点都在回归直线附近
④在平面直角坐标系中,直线
:
经过变换
后得到直线
的方程:
;
①在回归直线方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb33a6fc2f5856720b6d90ff5c2eee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8742381f1be13d88f51aa145522e5fe.png)
②残差平方和越小的模型,拟合的效果越好;
③散点图中所有点都在回归直线附近
④在平面直角坐标系中,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb976166ed146d11dd07923c5615b7df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2782067dc3e86d9da43090a53e378fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7e9d0e80d06d85627b9dca9e2aba1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2021-08-27更新
|
250次组卷
|
2卷引用:宁夏海原第一中学2020-2021学年高二下学期第二次月考数学(文)试题
名校
解题方法
5 . 对于椭圆
,令
,
,那么在坐标系
中,椭圆经伸缩变换得到了单位圆
,在这样的伸缩变换中,有些几何关系保持不变,例如点、直线、曲线的位置关系以及点分线段的比等等;而有些几何量则等比例变化,例如任何封闭图形在变换后的面积变为原先的
,由此我们可以借助圆的几何性质处理一些椭圆的问题.
(1)在原坐标系中斜率为k的直线l,经过
,
的伸缩变换后斜率变为
,求k与
满足的关系;
(2)设动点P在椭圆
上,过点P作椭圆
的切线,与椭圆
交于点Q,R,再过点Q,R分别作椭圆
的切线交于点S,求点S的轨迹方程;
(3)点
)在椭圆
上,求椭圆上点B,C的坐标,使得△ABC的面积取最大值,并求出该最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8429aec72d26401b12a55b8337261df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070cb835e194f9bb99aba9daf58bd2b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50443405ab95a95149c68f59f96619de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/863b5f9f0a7c6b7956979a5abc76d8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e08c4a230e32f550374a5fa4db5f204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848d4055ca831ecde46d1b666ba9e33d.png)
(1)在原坐标系中斜率为k的直线l,经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070cb835e194f9bb99aba9daf58bd2b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50443405ab95a95149c68f59f96619de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc8ced3660dab6e343773fd9dccebc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc8ced3660dab6e343773fd9dccebc3.png)
(2)设动点P在椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841307fdcdbbccacd07b652db535631f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd76519af3c3a098a590ad302acc003b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad492d5033448d419df9c9b75a71894e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
您最近一年使用:0次