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Why is the parameter T
Suppose that a straight line passes through the fixed point P(x0, y0), the corresponding parameter of A is t 1, and the corresponding parameter of B is t2.

And |AP|=|t 1|, |BP|=|t2| (sketch) hypothesis |t 1| > |t2|,

When A and B are on the same side of P, t 1, t2 is the same symbol, | AB | =| AP |-BP | =| T1| | T2 | = | T1-T2 |.

When A and B are on the opposite side of P, and t 1 and t2 are different, | AB | =| AP |+BP | = | T1|+T2 | = | T1-T2 |.