let M be (x,y)
AM.BM
= (x+1,y).(x-1,y)
= x^2+y^2 -1
|MC|^2 = x^2+(y-1)^2
AM•BM等于点M到点C(0,1)距离平方的k
=>
x^2+y^2 -1 = k( x^2+(y-1)^2)
(k-1)x^2 + (k-1)y^2-2ky +(k+1) =0