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

Geometry Level 4

Consider the circle x2+y2=9{ x }^{ 2 }+{ y }^{ 2 }=9 and the parabola y2=8x{ y }^{ 2 }=8x. They intersect at PP and QQ in the first and fourth quadrant respectively. The tangents to the circle at PP and QQ intersect the xx-axis at RR and tangents to the parabola at PP and QQ intersect thexx axis at SS. Then the ratio of areas of ΔPQS\Delta PQS and ΔPQR\Delta PQR is a:ba:b, where aa and bb are coprime positive integers. Find a+ba+b.

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