| | | | | 平面曲线的切线 | | | 曹发祯 | | | 平面解析几何对“求过二次曲线外的点所引曲线切线的方程”的问题,未给出一般的方法和公式。本文借助简单的微分运算对这一问题给出一种解决办法,并对一般的平面曲线的切线作了初步讨论。
【关键词】：二次曲线;平面曲线;切线方程
【DOI】：cnki:ISSN:1008-018X.0.1992-06-011
【正文快照】：
1 二次曲线的切线 众所周知,二次曲线 F@,y)一口1lz。+2a12zy+口22,+2a~3x+2a.y+口3I=0 (1)又称圆锥曲线.它是平面解析几何的主要研究对象.而求由曲线(1)所在平面上的一点M(Xo,yo)向曲线(1)所作的切线方程,又是研究二次曲线的一个重要内容.当点M在fHl线(1)上时,在中学已作了比较透沏的研究,且有相应的计算公式.但当点M不在曲线(1)上时,情况便比较复杂,在中学只能运用一些特殊技巧进行特殊的处理,且往往会遇到繁复的计算还很难推导出统一的计算公式.而到了大学,由于平面解析几何已不再作为教学内容,因而在学生头脑中便始终留下了一个理论… | | |  推荐 CAJ下载  PDF下载 | | | CAJViewer7.0阅读器支持所有CNKI文件格式，AdobeReader仅支持PDF格式 | | | | The Tangent of a Plane Curve | | | Cao Fazhen | | | The problem of attaining the tangent equation of a certain point on a quadratic curve is basically solved in plane analytical geometry. But there hasn't been a general solution to the problem of attaining the tangent equation of the curve that is deduced from a point outside a quadratic curve , and a general appropriate formula is not mentioned either.
In this paper , by means of simple differential operations, a perfect solution to the second problem stated above is presented . And the problem of attaining the tangent of a general plane curve is discussed elementarily.
【Keyword】：quadratic curve , plane curve , tangent equation |
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