Let $$P$$ be the point on the parabola $$y=x^2$$ such that the slope of the tangent to the parabola at the point $$P$$ is $$4$$. Let $$Q$$ be the point in the first quadrant lying on the circle $$x^2+y^2=2$$ such that the slope of the tangent to the circle at the point $$Q$$ is $$-1$$. Let $$R$$ be the point in the first quadrant lying on the ellipse $$x^2+4y^2=8$$ such that the slope of the tangent to the ellipse at the point $$R$$ is $$-\tfrac{1}{2}$$. Then the radius of the circle passing through the points $$P,Q$$ and $$R$$ is