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 \( -\frac{1}{2} \). Then the radius of the circle passing through the points \( P, Q \) and \( R \) is:
