one correction,
it should be |y| =|x|+2
IF a point moves such that twice its distance from axis of x exceeds its distance from axis of y by 2,then its locus is
Let the point have co-ordinates (h,k)
SO, k=h+2 ( by condition)
thus the locus of the point is y=x+2.( replacing h by x and k by y).