AB中点P(x,y)
xA+xB=2x
yA+yB=2y
过Q(2,-4)的圆O:x^2+y^2=9的割线AB:
x=2,y=-4,这时AB的中点为x=2,y=0
x≠2,y+4=k(x-2)
k=(yA-yB)/(xA-xB)=(y+4)/(x-2)
割线,交圆O于点A,B
x^2+y^2=9
(xA)^2+(yA)^2=9.(1)
(xB)^2+(yB)^2=9.(2)
(1)-(2):
(xA+xB)*(xA-xB)+(yA+yB)*(yA-yB)=0
(xA+xB)+(yA+yB)*[(yA-yB)/(xA-xB)]=0
2x+2y*(y+4)/(x-2)=0
x^2-2x+y^2+4y=0
点P的轨迹方程:(x-1)^2+(y+2)^2=5或一个点x=2,y=0