Area Under The Curves

If the points of intersection of two distinct conics \(x^2+y^2=4 b\) and \(\frac{x^2}{16}+\frac{y^2}{b^2}=1\) lie on the curve \(y^2=3 x^2\), then \(3 \sqrt{3}\) times the area of the rectangle formed by the intersection points is _________.