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  4. Consider the circle x2+y2=9 and the parabola y2=8 x. They intersect at P and Q in the first and the fourth quadrants, respectively. 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. The radius of the circumcircle of the triangle PRS is

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Q. 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 fourth quadrants, respectively. 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 $S$.
The radius of the circumcircle of the triangle PRS is

JEE AdvancedJEE Advanced 2007

Solution:

The circumcircle of $\triangle PRS$
is $(x+1)(x-9)+y^{2}+\lambda y=0$
It will pass through the point $(1,2 \sqrt{2})$. Then,
$\lambda=2 \sqrt{2}$
The equation of circumcircle is
$x^{2}+y^{2}-8 x+2 \sqrt{2} y-9=0$
Hence, its radius is $3 \sqrt{3}$.