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在三角函数和解析几何的学习中,我们会碰到一类与过角内定点的直线有关的极值问题.例如:已知直线l过点P(3,2),且与x轴正半轴、y轴正半轴分别交于A,B两点.据此,我们可以求:(1)△AOB面积的最小值;(2)截线段积PA·PB的最小值;(3)截线段和OA+OB的最小值.但更具探究和拓展价值的是:求截线段和PA+PB的最小值.
In the study of trigonometric functions and analytic geometry, we encounter a class of extremum problems related to the straight line of the overactive vertex, for example, it is known that the straight line l passes P (3,2) Axis and the positive y-axis are respectively intersected with point A and point B. Therefore, we can find: (1) the minimum value of △ AOB area; (2) the minimum value of the sectional line product PA · PB; (3) Line segment and OA + OB minimum.But more to explore and expand the value of: seeking the minimum value of the line segment and the PA + PB.