点到直线的距离公式,是解析几何中的重要公式。公式的应用有些时候是显性的,容易发现的;有些时候是隐性的,不易发现的。本文探讨的主要是隐性问题,也即需要构造点到直线距离问题——通过构造,开辟解题的新天地,通过构造,快速地解决问题。例1设f(x)=(-x2-4x)1/2,g(x)=4/3x+1-a,若恒有f(x)≤g(x)成立,求实数a的取值范围。 The point-to-line distance formula is an important formula in analytic geometry. The application of the formula is sometimes dominant, easy to find; sometimes implicit, not easy to find. This article mainly discusses the hidden problems, that is, the problem of constructing the point-to-line distance needs to be solved - by constructing and opening up a new world of problem solving, the problem can be solved rapidly through construction. Example 1 Suppose f (x) = (-x2-4x) 1/2, g (x) = 4 / 3x + 1-a, and if f (x) ≤g Value range.