QJEEAdv07Ma82fe: JEE Advanced 2007 Mathematics - Class 11 JEEAdv07Ma82fe Solution: Consider the circle x 2 + y 2 = 9 and the parabola y 2 = 8 x .…

Consider the circle $$x^2+y^2=9$$ and the parabola $$y^2=8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, respectively. Tangent 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 incircle of the triangle $$PQR$$ is