设圆心的坐标为(a,b),圆半径为r.
∵ 圆心必在pq的中垂线上,而pq的中垂线方程为
y-5/2 = 5(x-3/2)
∴ b = 5a-5 ,且 r² = (a-4)²+(b-2)² = 13(2a²-6a+5)
圆的方程为
(x-a)²+(y-b)² = r²
四个截距为
x = a±√(r²-b²) ,y = b±√(r²-a²)
和是
2a+2b = 2 a+b = 1
得 5a-5+a = 1 ,a = 1 ,b = 5a-5 = 0 ,r = √13×1 = √13
∴ 圆的方程为
(x-1)²+y² = 13