1 . (1)在平面直角坐标系中,求下列方程所对应的图形经过伸缩变换
后的图形.
①
;
②
.
(2)伸缩变换的坐标表达式为
,曲线
在此变换下变为椭圆
,求曲线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a5bfd4582b7fe96534c6b1704bc319.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810738c63815bffe59d99eb1cef20e21.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64b7ab668d61bcb8ec6d195c672a81e.png)
(2)伸缩变换的坐标表达式为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547d7306612e299576493b1cdd704ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fcbc0a937609a8591ea78428433ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2 . 在同一平面直角坐标系中,已知伸缩变换
.
(1)求点
经过变换
所得的点
的坐标;
(2)点
经过变换
得到点
,求点
的坐标;
(3)求直线
经过变换
后所得直线
的方程;
(4)求双曲线
经过变换
后所得曲线
的焦点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6440c5f31f9e639e0138ad7216c042.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf97eea4e3024c0b34343d004a526af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d7ffb7889a31b267a85f1ea238138e.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f56232f1894c6c68197bed9e17b4da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a42751b87ccc37039057c71b12571f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354f8e9d6cca157b95877d6540d16fb3.png)
(4)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7278e51850c994afe4f64ca793fe7555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3557809c066e68395b614535a7675e76.png)
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3 . 设曲线
经过伸缩变换
之后,变成双曲线
,求这个伸缩变换
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0ca78fe585338f922b3fc7bcf1e193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
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4 . 在平面直角坐标系中,求下列曲线方程所对应的图形经过伸缩变换
后的图形.
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9814fd831c7eb70929219e6453c6e484.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
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5 . 在
中,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7105465941e9c130703b15790c6c1ecf.png)
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6 . 已知点
的坐标是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d739c713e04e7c5bcdd7036894381fa4.png)
都是有理数,
分别是点
到
轴和
轴的垂线段,且矩形
(
为坐标原点)的面积为
,则点
可能出现在第几象限?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d739c713e04e7c5bcdd7036894381fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e902eb263971b466d0fcd91c56b453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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7 . 求函数
经伸缩变换
后的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b41a628c4b3053a9f9669ba21e657f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdcc5ae338fcb329f95055634640bf87.png)
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8 . 已知函数
的图象经过坐标变换得到函数
的图象,求该坐标变换.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18855961bf2f4310ef97057c8ed83f0.png)
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9 . 在同一平面直角坐标系中,经过伸缩变换
后,曲线
变为曲线
,求曲线
的方程,并判断其形状.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827a8e083f1cede8a016204efd5f4bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75c40fb96da3748c1796204a2c0a7c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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