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在数学问题的解决中,等价转化与数型结合思想有着极其重要的应用,尤其在一定条件下,求某些式子的最值问题,就可利用数形结合的方法,转化为求斜率、截距、距离等问题,从而使问题得到解决．一、转化为直线的斜率例1 如图1,若实数x,y满足(x-2)2+y2 =3,求y/x的最大值及最小值. 点拨:点(x,y)满足圆的方程,而y/x正是圆上的点与原点连线的斜率．如果把(x,y)视为动点,借助图形观察,则y/x的最大值和最小值正是由原点向圆所引的两条切线的斜率．
In solving mathematical problems, equivalent transformation and the combination of number has an extremely important application of the idea, especially under certain conditions, seeking the most value of some formula problem, you can use the method of combination of number form, into the slope , Intercept, distance and other issues, so that the problem is solved. First, the slope of the conversion into a straight line Example 1 As shown in Figure 1, if the real number x, y satisfy (x-2) 2 + y2 = 3, find the maximum and minimum y / x. The equation of the circle, and y / x is the slope of the line connecting the point on the circle to the origin. If (x, y) is treated as a moving point, the maximum and minimum values of y / x are exactly the slopes of the two tangent lines from the origin to the circle.