I have a .txt file from which I find ordered pairs, and then draw a graphic using numpy and matplotlib. For example these are my ordered pairs:
[[(4.0, 0), (0, 6
Maybe you can take a look on "sage". Sage is an opensource computer algebra system and you can nearly verything eg. Graphtheorie and Plotting like a boss. http://www.sagemath.org/
You can start by trying SymPy for intersection (specifically) here.
There is more to SymPy; it will fit most of the things you might want to do! Read the docs for all of its capabilities.