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与圆有关的最值问题是一类热点问题,常见解法是观察所给式子的几何意义,充分利用圆的性质,由数形结合来解决。一、与圆上的点的坐标有关的最值问题例1设实数x、y满足x2+(y-1)2=1,求(y+2)/(x+1)的最值。分析:(y+2)/(x+1)的几何意义是圆上一动点(x,y)与已知定点(-1,-2)连线的斜率。
The most value problem related to circles is a kind of hot issues. The common solution is to observe the geometric meaning of the given formulas, make full use of the nature of the circle, and solve it by the combination of number and form. First, the coordinates of the point on the circle with the most value Problem Example 1 Let the real number x, y satisfy x2 + (y-1) 2 = 1, find (y +2) / (x +1) the most value. Analysis: The geometric meaning of (y + 2) / (x + 1) is the slope of the line connecting the point (x, y) on the circle and the known fixed point (-1, -2).