# Sliding Lines

Calculus Level 4

Two lines have the following equations (assuming $$p = (x, y)$$):

$$n_1 \cdot (p - p_1(t) ) = 0$$

with $$n_1 = (1, 2) , p_1(t) = (1, 1) + (1, 3) t$$ , and

$$n_2 \cdot (p - p_2(t) ) = 0$$

with $$n_2 = (1, -1), p_2(t) = (-1,1) + (1, -1) t$$

$$t$$ is the time parameter. The intersection of these two lines traces a line (shown in red in the animation). If the slope of the traced line is $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a + b$$

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