Let $a, r, s, t$ be nonzero real numbers. Let $P(at^2, 2at)$, $Q$, $R(ar^2, 2ar)$ and $S(as^2, 2as)$ be distinct points on the parabola $y^2 = 4ax$. Suppose that $PQ$ is the focal chord and lines $QR$ and $PK$ are parallel, where $K$ is the point $(2a, 0)$.
The value of $r$ is\\
(A) $-\frac{1}{t}$\\
(B) $\frac{t^2+1}{t}$\\
(C) $\frac{1}{t}$\\
(D) $\frac{t^2-1}{t}$