Consider the circle \( x^{2}+y^{2}=9 \) and the parabola \( y^{2}=8 x \). They intersect at \( P....

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Consider the circle \( x^{2}+y^{2}=9 \) and the parabola \( y^{2}=8 x \). They intersect at \( P \) and \( Q \) in the first and the
\( \mathrm{P} \)
fourth quadrants, respectively. The tangents to the
W
circle at \( P \) and \( Q \) intersect \( x \)-axis at \( R \) and tangents to the parabola at \( P \) and \( Q \) intersect \( x \)-axis at \( S \).
Answer the following questions.
The ratio of the areas of \( \triangle P Q S \) and \( \triangle P Q R \) is:
(1) \( 1: \sqrt{2} \)
(2) \( 1: 2 \)
(3) \( 1: 4 \)
(4) \( 1: 8 \)
.


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