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

Geometry Level 4

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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