过点P（2,4）及Q（3,-1）两点,且在X轴上截得的线段长为6的圆的方程是

（5/2,3/2)
k=5/-1=-5
k=1/5
y-3/2=1/5(x-5/2)
/y/^2+3^2=(x-2)^2+(y-4)^2
y^2+9=(x-2)^2+y^2-8y+16
(x-2)^2-8y+7=0
y=3/2+1/5(x-5/2)
(x-2)^2-12-8/5(x-5/2)+7=0
5(x-2)^2-60-8(x-5/2)+35=0
5x^2-20x+20-60-8x+20+35=0
5x^2-28x+15=0
（5x-3)(x-5)=0
x=3/5,x=5
y=3/2+1/5(3/5-5/2)=112/100=28/25
(3/5,28/25)
(5,2)
(x-3/5)^2+(y-28/25)^2=(3/5-2)^2+(28/25-4)^2
(x-5)^2+(y-2)^2=13