Containment problem for points on a reducible conic in P²

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Given an ideal I in a Noetherian ring, one can ask the containment question: for which m and r is the symbolic power I⁽ᵐ⁾ contained in the ordinary power Iʳ? C. Bocci and B. Harbourne study the containment question in a geometric setting, where the ideal I is in a polynomial ring over a field. Like them, we will consider special geometric constructs. In particular, we obtain a complete solution in two extreme cases of ideals of points on a pair of lines in P²; in one case, the number of points on each line is the same, while in the other all the points but one are on one of the lines.