maximum number of collinear points? I know this is a very standard question widely popular in the Internet and the Mathworld.
I myself have solved the above problem is N^2 Log N avoiding floating arithmetic.However, can anyone give me a good resource/detailed explanation of how it can be solved in O(N^2) using point line duality concepts.

Sorry to create such a confusion regarding the statement.
The text would be:
"N different points with integer coordinates are given in a plane. You are to write a program that finds the maximum number of collinear points (they all belong to the same line)."

You may also refer to this site which is the problem I have solved using a N^2Log N approach.
By point-line duality, this is equivalent to the question 'given a configuration of $n$ lines in the plane, what is the maximum number of them which intersect at one point?'; since there are $O(n^2)$ pairwise intersection checks, it becomes a question of whether there's some bucketing/perfect hashing scheme that allows for finding a point in a dynamically-built list in $O(1)$ time.  While I don't know of any specific bucketing schemes applicable to this problem, AFAIK it's very common to have $O(1)$ or at least $O(\alpha(n))$ approaches for this sort of thing ($\alpha(n)$ being the inverse-Ackermann function).
The maximum number of collinear points among N points in a plane is N (i.e., if they happen to be collinear.)