Functions, Relations & Transformations · Superchallenge problem

A dilation with centre $(p, q)$ and ratio $r > 0$ moves each point $P$ to the point $P'$ on ray $CP$ (where $C = (p, q)$) with $CP' = r\cdot CP$. Exactly one such dilation maps the parabola $y = x^2$ onto the parabola $y = 3x^2 - 12x + 5$. Find $p + q$.