be a monic polynomial with integer coefficient. And suppose there exist 4 distinct integer 
such that 
.
such that 
such that ![\[f(2x+y) + f(x+f(2y)) = f(x)f(y) - xy\]](http://latex.artofproblemsolving.com/0/6/2/0623b7c328af6d088cfc5dd288afe3e17a94ff29.png)
for all reals 
and 
.
sastifying 
Y by
The ''distance'' 
between two points 
in the 
-plane is defined by 
. Using this notion of distance, find the locus of all points satisfying 
and which are equidistant from the origin and from a fixed point 
in the plane, where 
. Distinguish the cases acoording to the signs of 
and 
.
between two points 
in the 
-plane is defined by 
. Using this notion of distance, find the locus of all points satisfying 
and which are equidistant from the origin and from a fixed point 
in the plane, where 
. Distinguish the cases acoording to the signs of 
and 
.
