“圆是最美的图形”!有一类代数题目,如果我们将它的题设做换元,转化为直角坐标系下圆的方程,用直线与圆的位置关系求解,会变得直观而简捷.一、求取值范围例1(第19届“希望杯”高二试题)已知1-3b,2a,1+3b成等比数列,求8a+9b的取值范围.解:依题设应有(2a)~2+(3b)~2=1(a≠0),设 There is a class of algebraic problems that can be intuitively solved if we convert it to a discourse under the Cartesian coordinate system and solve it by solving the relationship between the straight line and the circle Example 1: Find the range of values ​​of 8a + 9b for 1-3b, 2a, 1 + 3b, which is known from the 19th “Hope Cup” According to the hypothesis should have (2a) ~ 2 + (3b) ~ 2 = 1 (a ≠ 0), set