Let \( a, r, s \) and \( t \) be non-zero real numbers. Let \( P\left(a t^{2} 2 a t\right) \),
P \( Q\left(\frac{a}{t^{2}}, \frac{-2 a}{t}\right), R\left(a r^{2}, 2 a r\right) \) and \( S\left(a s^{2}, 2 a s\right) \) be distinct points
W on the parabola \( y^{2}=4 a x \). Suppose that \( P Q \) is the focal chord and lines \( Q R \) and \( P K \) are parallel, where \( K \) is the point \( (2 a, 0) \).
The value of \( r \) is
(a) \( -\frac{1}{t} \)
(b) \( \frac{t^{2}+1}{t} \)
(c) \( \frac{1}{t} \)
(d) \( \frac{t^{2}-1}{t} \)
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