AB中点M(x,y)
xA+xB=2x,yA+yB=2y
(xA+xB)^2=(2x)^2
(xA)^2+(xB)^2+2xA*xB=4x^2.(1)
(yA)^2+(yB)^2+2yA*yB=4y^2.(2)
(xA)^2+(yA)^2=9.(3)
(xB)^2+(yB)^2=9.(4)
PA⊥PB
k(PA)*k(PB)=-1
[(yA-2)/(xA-1)]*[(yB-2)/(xB-1)]=-1
2xA*xB+2yA*yB=2[(xA+xB)+2(yA+yB)-5]=4x+8y-10.(5)
(1)+(2)-(3)-(4)-(5):
4x^2+4y^2-4x-8y-8=0
AB中点M的轨迹方程圆:
(x-0.5)^2+(y-1)^2=3.25