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Let \( a, r, s, t \) be nonzero real numbers.
\( \mathrm{P} \)
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 \( (2 a, 0) \).
If \( s t=1 \), then the tangent at \( P \) and the normal at \( S \) to the parabola meet at a point whose ordinate is:
(1) \( \frac{\left(t^{2}+1\right)^{2}}{2 t^{3}} \)
(2) \( \frac{a\left(t^{2}+1\right)^{2}}{2 t^{3}} \)
(3) \( \frac{a\left(t^{2}+1\right)^{2}}{t^{3}} \)
(4) \( \frac{a\left(t^{2}+2\right)^{2}}{t^{3}} \)
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