Let the co-ordinate of the point be (h,k)
Let the co-ordinate of the point of intersection with the Axes be ( x,0) and (0,y)
By the given ratio of 1:2 section formula:
So, 2y/3= k and x/3 = h
So y= 3k/2 and x= 3h
Now
Therefore
Required locus is
.