# Example for intersection, multiplicity and tangents for projective plane curves

We recently got introduced to projective plane curves in our class, however we just defined it and never really talked about examples. And when I am trying to come up with a just any curve, calculating the multiplicity at a point is rather hard (in comparison to the affine case at least). So could someone give me a simple (but not completely trivial) example of $$1$$ or $$2$$ curves and calculate multiplicities, tangents and/or the intersection of them. Thank you in advance!