Let's intersect them!(For JEE ADV 2016)

Geometry Level 5

Consider the circle \({ x }^{ 2 }+{ y }^{ 2 }=9\) and the parabola \({ y }^{ 2 }=8x\). They intersect at \(P\) and \(Q\) in the first and fourth quadrant respectively. The tangents to the circle at \(P\) and \(Q\) intersect the \(x\)-axis at \(R\) and tangents to the parabola at \(P\) and \(Q\) intersect the\(x\) axis at \(S\). Then the ratio of areas of \(\Delta PQS\) and \(\Delta PQR\) is \(a:b\), where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

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