将y=x-1代入圆方程,得到:2x^2-2(a+1)x+a^2+1-r^2=0。故Px=(x1+x2)/2=(a+1)/2;Py=(a-1)/2。依题意:(a-1)/(a+1)=1/3,解得a=2。
AB^2=2[x1-x2]^2=2[(x1+x2)^2-4x1x2]=2[(a+1)^2-4(a^2+1-r^2)]=20.......(1)又OA⊥OB,所以
x1*x2+y1*y2=0,即2x1x2-(x1+x2)+1=0。故2[a^2+1-r^2]-(a+1)+1=0.........(2)联立(1)(2)解得:a=3或-3.相应r^2=7或13,所以圆的方程为:
(x-3)^2+y^2=7或(x+3)^2+y^2=13
能求出P点坐标