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For the lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 to be parallel, the condition is:

Aa1/a2 = b1/b2

Ba1*a2 + b1*b2 = 0

Ca1*b2 = -a2*b1

Da1/b1 = a2/b2