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解析几何的本质是用代数方法研究几何图形的性质,即通过直角坐标系,建立点与坐标、曲线与方程之间的对应关系,将几何问题转化为代数问题,从而用代数方法研究几何问题。故在遇到求取值范围的问题时,我们常常会引入变量,通过构建函数,将问题转化为求函数的值域。此时,需要关注的是,一定要考察变量的选取及变量的范围,下面通过例题进行说明。
The essence of analytic geometry is to study the properties of geometry by algebraic method. That is to say, through the rectangular coordinate system, the correspondence between points and coordinates, curves and equations is established, and the geometric problems are transformed into algebraic problems. Therefore, in the face of the problem of the range of values, we often introduce variables through the construction of the function, the problem is converted to the range of functions. At this point, we need to pay attention, we must examine the variable selection and variable range, the following examples to illustrate.