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Let \( a, r, s, t \) be nonzero real numbers.
P
Let \( P\left(a t^{2}, 2 a t\right), Q, R\left(a r^{2}, 2 a r\right) \) and \( S\left(a s^{2}, 2 a s\right) \) be distinct
W points 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:
(1) \( -\frac{1}{t} \)
(2) \( \frac{t^{2}+1}{t} \)
(3) \( \frac{1}{t} \)
(4) \( \frac{t^{2}-1}{t} \)
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