Geometry Level pending

A parabola is defined parametrically by the following system of equations:

$$\begin{cases} x = (3t-1)(t-1)+\mathcal{C}_1\\ y = (2t+1)^2 + \mathcal{C}_2 \end{cases}$$

If the Latus Rectum can be expressed as $$\dfrac{a^p \times b^q}{c^r}$$, where $$a,b,c$$ are prime numbers, and $$p,q,r$$ are positive integers, find the value of $$ap+bq+cr$$

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