Projective stuff... Great
From what I can recall, a line passes through every two points.
For the total number of lines, define a_ij to indicate the line passing through points i and j. All lines have N+1 points; So the cardinality of (a_ij) is (N+1)^2. But also, the diagonal (a_ii) does not define a line; So exclude N lines from this list, to get a total of (N+1)^2-N=N^2+N+1 lines.
For the number of points, I think there should be more than just N^2+N+1... Check again plz.