设P(x,y),
PO^2=x^2+y^2
PA^2=x^2-2cx+c^2+y^2
|PO^2-PA^2|=c
|2cx-c^2|=c
4c^2x^2-4c^3x+c^4=c^2
c=0,不合题意,c≠0
4x^2-4cx+c^2-1=0
[2x-(c+1)][2x-(c-1)]=0
∴x=(c+1)/2,x=(c-1)/2 .