问题 一条直线L经过点P(2,1),且与x 轴正半轴、y轴正半轴交于B、C两点.如果三角 形BOC的面积最小,求此直线L的方程. 此题是本刊2004年第7月上期《一个解析 几何问题的解法及启示》中的问题.它给出了多 种解法以及启示,写得很好.但在问题的多种解 法中,本人认为还有一种常见的通解,没有给出, 应值得一提. 解法 (待定系数法) 利用直线的截距式, 以及不等式的性质定理:两个正变量的和是常 量,积有最大值. 解 设直线方程为x/a+y/b=1(a>0,b>0). A line L passes through point P(2,1) and intersects the positive x-axis and the positive y-axis at B and C. If the area of ​​the triangle BOC is the smallest, find the equation for this line L. This is the problem in the last issue of “A Solution to Geometric Problems and Its Enlightenment” in the last issue of the magazine in July of 2004. It gives a variety of solutions and inspirations. It is well written. But in the various solutions of the problem, I believe that There is a common general solution, which is not given. It should be worth mentioning. The solution (the coefficient to be determined) uses the intercept of the line, and the property theorem of inequality: the sum of two positive variables is a constant and the product has a maximum. The linear equation is x/a+y/b=1 (a>0, b>0).