圆是最常见的简单几何图形,因其自身独特的几何特征,所以在做题时要注意数形结合思想的运用,充分利用图形的性质,不仅可以减少运算量,节省时间,而且还可以提高准确度,更能达到事半功倍的效果,下面举例说明。例1如图1,求圆x2+y2=4上的点到直线4x+3y-12=0的最短距离。解析:圆心(0,0)到直线4x+3y-12=0的距离为d=|4×0+3×0-12|/(42+32)1/2=12/5。 Circular is the most common simple geometry, because of its own unique geometric characteristics, so in the question should pay attention to the use of mathematical combination of ideas, take full advantage of the nature of graphics, not only can reduce the amount of computation, save time, but also can improve Accuracy, better able to achieve a multiplier effect, the following examples. Example 1 In Figure 1, find the shortest distance from the point on the circle x2 + y2 = 4 to the straight line 4x + 3y-12 = 0. Resolution: The distance from the center of the circle (0,0) to the straight line 4x + 3y-12 = 0 is d = | 4 × 0 + 3 × 0-12 | / (42 + 32) 1/2 = 12/5.