設(shè)圓心的坐標(biāo)為(a,b),圓半徑為r.
∵ 圓心必在pq的中垂線上,而pq的中垂線方程為
y-5/2 = 5(x-3/2)
∴ b = 5a-5 ,且 r² = (a-4)²+(b-2)² = 13(2a²-6a+5)
圓的方程為
(x-a)²+(y-b)² = r²
四個(gè)截距為
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
∴ 圓的方程為
(x-1)²+y² = 13