1.设圆心C(0,b),圆的方程为x² + (y-b)² = 25
代入(-3,2):9 + (2-b)² = 25
b = 6或b = -2
圆的方程为x² + (y -6)² = 25或x² + (y+2)² = 25
2.设圆心(a,b),半径r
（x-a)² + (y-b)² = r²
代入3点的坐标：
（a+1)² + (b-1)² = r² (1)
(a-4)² + (b-1)² = r² (2)
(a+1)² + (b-4)² = r² (3)
由(1)(2): (a+1)² = (a-4)²
a + 1 = a - 4 (无解)
或a+1 = 4-a,a = 3/2
类似,由(1)(3),b = 5/2
r² = 17/2
(x - 3/2)² + (y - 5/2)² = 17/2
3.原点和A(1,1）的中点为B(1/2,1/2),OA的斜率为(1-0)/(1-0) = 1
OA的中垂线的斜率为-1,方程为y - 1/2 = -(x - 1/2),y = 1 -x
与2x + 3y + 1 = 0联立,可得圆心为C(4,-3)
半径=OC=√(4-0)²+(-3-0)² = 5
圆的方程:(x-4)² + (y+3)² = 25