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在学习解析几何时,一部分学生并没有真正理解解析几何研究问题的方法与思路,总是忽视几何对象本身的性质,盲目地进行代数运算,尤其是涉及直线与圆锥曲线的问题时更为突出。学生总是机械性地联立直线与圆锥曲线的方程,导致运算量大、越做越茫然,甚至出现本质上的错误。本文以“直线与椭圆的位置关系”一节为例,从分析曲线的代数结构特征人手,利用数形结合,对直线与椭圆的几何性质从不同角度进行层层剖析,帮助学生进一步理解并感悟解析几何的思维本质,走出解析几何学习的误区。
When studying analytic geometry, some students did not really understand the methods and ideas of analytic geometry research. They always ignored the properties of geometric objects and performed algebra blindly, especially when it came to the problems of straight lines and conic curves. Students always mechanically combine the straight line with the conic equation, resulting in a large amount of computation, more and more dazed, and even an essential error. In this paper, we take “the relation between the position of a straight line and an ellipse” as an example. By analyzing the algebraic structural features of the curve, we use the combination of number and form to analyze the geometrical properties of straight lines and ellipses from different perspectives and help students to further understand And sentiment analysis of the nature of the thinking of geometry, geometry analysis out of misunderstanding.