Meta-Quadratic Parametric

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 $ap+bq+cr$