Universal hashing

You are given a set of n points in the 2D plain;. Each point p_i is given by its x and y coordinates (x_i, y_i). Two points are called identical if one is obtained from the other by multiplication by the same number (scalar multiplication). So for example (10, 15), (2, 3) and (100, 150) are identical, but (10, 15) and (10, 20) are not. (a) Suggest an algorithm that runs in worst case time O(n log n) and determines whether the input contains two identical points. That is, whether among the n points, you could find a pair which is identical. (b) Repeat, but now the expected running time is O(n)