Question 152311
Let x and y the center of the moving circle
then distance between (x,y)and x-axis = distance between (x,y)and (2,-6)-1
Obs: y<0

d((x,y),(x,0))=d((x,y),(2,-6))-1
-y+1=d((x,y),(2,-6))
[-y+1]^2=[d((x,y),(2,-6))]^2
y^2-2y+1=(x-2)^2+(y+6)^2

y^2-2y+1=x^2-4x+4+y^2+12y+36


-2y+1=x^2-4x+4+12y+36

-14y-x^2+4x-39=0

(check your solution please)