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解析几何是高中的一门重要的基础学科,共有39个知识点（其中直线占11个、圆锥曲线占20个、参数方程、极坐标占8个）,它的基本特点是形数结合,是代数、三角、几何知识的综合应用。纵观近几年高考试题,解几内容不仅占有相当比重,而且常被作为综合考察学生能力的重要内容。根据对1990——1994年高考试题中解几内容的分析解析,几何热点问题有:一是直线的位置关系;二是直线与圆锥曲线的位置关系;三是双二次曲线间的关系;四是参数方程、极坐标的基本概念、基础知识、基本运算。现以上述四个方面所涉及的考点进行分析研究,并以高考试题为例说明。一、直线的位置关系直线是解析几何的基础,其能力要求的层次主要是理解、掌握的层次,但对线段中点公式、两点间距离则要求能熟练应用。近年高考试题也充分体现了考试说明中对此部分内容的要求、多以选择题、填空题的形式出现,但也出现过以直线内容来考察综合应用知识解决问题能力的试题。
Analytic geometry is an important basic subject of high school. There are 39 knowledge points (including 11 straight lines, 20 conic curves, 8 parametric equations, and 8 polar coordinates). Its basic feature is the combination of shapes and numbers. Comprehensive application of algebra, trigonometry and geometry knowledge. Looking at the examination questions in recent years, the solution of several contents not only occupies a considerable proportion, but is often used as an important part of a comprehensive survey of student abilities. According to the analysis of several contents in the 1990-1994 high exam questions, the geometric hot issues include: first, the positional relationship of the straight line; second, the positional relationship between the straight line and the conic curve; and third, the relationship between the two conic curves; It is the basic concept, basic knowledge and basic operation of parametric equations and polar coordinates. The analysis of the test sites involved in the above four aspects is now carried out, and examples of high test questions are used as examples. First, the positional relationship of the straight line is the basis of analytic geometry, the level of its ability requirements is mainly to understand, grasp the level, but the midpoint formula of the line segment, the distance between the two points requires skilled application. In recent years, the high examination questions also fully reflected the requirements of this part of the examination description, mostly in the form of multiple-choice questions and blank-filling questions. However, there have also been examination questions in which straight-line contents are used to examine comprehensive application knowledge to solve problems.