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Let \( a, r, s \) and \( t \) be non-zero real numbers. Let \( P\left(a t^{2} 2 a t\right) \),
\( \mathrm{P} \) \( Q\left(\frac{a}{t^{2}}, \frac{-2 a}{t}\right), R\left(a r^{2}, 2 a r\right) \) 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 \( (2 a, 0) \)

If \( s t=1 \), then the tangent at \( P \) and the normal at \( S \) to the parabola meet at a point whose ordinate is
(a) \( \frac{\left(t^{2}+1\right)^{2}}{2 t^{3}} \)
(b) \( \frac{a\left(t^{2}+1\right)^{2}}{2 t^{3}} \)
(c) \( \frac{a\left(t^{2}+1\right)^{2}}{t^{3}} \)
(d) \( \frac{a\left(t^{2}+2\right)^{2}}{t^{3}} \)
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