Where does the hyper-plane begin with a SVM, an how does it iterate to it's ideal positioning?

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This is a little tricky for me to word and have been studying support vectors. I understand where the hyper-plane should should sit on a graph, but I can't seem to find how this process starts out.

Based on some initial classification data, where would say a computer choose to first draw a hyper-plane? and then what is the process for changing it's direction/position on a 2D graph?