P and Q are two points on the parabola y^2 = | vedclass

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(C) Let the points $P, Q, R, T$ on the parabola $y^2 = 4ax$ (where $a=2$) be represented by parameters $t_1, t_2, t_4, t_3$ respectively.Since $PS$ an

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$(-2, 3)$

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(C) Let the points $P, Q, R, T$ on the parabola $y^2 = 4ax$ (where $a=2$) be represented by parameters $t_1, t_2, t_4, t_3$ respectively.Since $PS$ and $QS$ are focal chords,we have $t_1 t_3 = -1$ and $t_2 t_4 = -1$.The equation of the chord $PQ$ is $y(t_1 + t_2) = 2x + 2a t_1 t_2$. Substituting $a=2$,we get $y(t_1 + t_2) = 2x + 4 t_1 t_2$.Since $PQ$ passes through $(-2, 3)$,we have $3(t_1 + t_2) = -4 + 4 t_1 t_2$.Substituting $t_1 = -1/t_3$ and $t_2 = -1/t_4$,we get $3(-1/t_3 - 1/t_4) = -4 + 4/(t_3 t_4)$.Multiplying by $t_3 t_4$,we get $-3(t_4 + t_3) = -4 t_3 t_4 + 4$,which simplifies to $3(t_3 + t_4) = 4 t_3 t_4 - 4$.The equation of the chord $TR$ is $y(t_3 + t_4) = 2x + 4 t_3 t_4$.Comparing this with the condition $3(t_3 + t_4) = 4 t_3 t_4 - 4$,we see that the line $TR$ passes through the point $(-2, 3)$.

$P$ and $Q$ are two points on the parabola $y^2 = 8x$ and $S$ is its focus. $PS$ and $QS$ meet the curve again in $T$ and $R$ respectively. If $PQ$ passes through a fixed point $(-2, 3)$,then $TR$ also passes through a fixed point whose coordinates are

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