Let \( a, r, s, t \) be non-zero real numbers. 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
point 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 point \( (2 a, 0) \). If \( s t=1 \), then the tangent at \( P \) and the normal at \( S \).
the parabola meet at a point whose ordinate is \( \begin{array}{ll}\text { (a) } \frac{\left(t^{2}+1\right)^{2}}{2 t^{3}} & \text { (b) } \frac{a\left(t^{2}+1\right)^{2}}{2 t^{3}}\end{array} \)
(I)
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