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仿射变换之化"椭"为"圆"的妙用

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仿射变换的一些重要性质在欧氏几何上有着很好的应用,以近几年高考真题为例,探讨研究了仿射变换在解决有关椭圆中求面积、直线斜率、最值、定值等一系列问题中的应用,化"椭"为"圆",巧妙地解决圆锥曲线的相关问题,给出了不同题型下灵活运用仿射变换的具体方法。
The Ingenious Application of Affine Transformation Through Turning"Ellipse"into"Circle"
Some important properties of affine transformations are commonly employed for solving issues in Euclidean geometry.Taking the real questions of recent college entrance examination as examples,this paper discusses the application of affine transformations in solving a series of problems related to finding area,slope of straight lines,extremum and constant values in ellipses.It ingeniously solves problems related to conic sections by transforming"ellipses"into"circles"and provides specific methods for flexible use of affine transformations in different types of problems.

affine transformationellipsecircle

白丽艳、殷秀仙、李江燕

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玉溪师范学院数理学院,云南玉溪 653100

仿射变换 椭圆

玉溪师范学院教学研究与改革实践项目课程思政示范课程建设项目

2022172022sz15

2024

玉溪师范学院学报
玉溪师范学院

玉溪师范学院学报

影响因子:0.144
ISSN:1009-9506
年,卷(期):2024.40(3)