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 circumcircle of the triangle $$PRS$$ is

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

STATEMENT-1: The curve $$y = {{ - {x^2}} \over 2} + x + 1$$ is symmetric with respect to the line $$x=1$$. because

STATEMENT-2: A parabola is symmetric about its axis.

$${{{d^2}x} \over {d{y^2}}}$$ equals