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If the points of intersection of two distinct conics $$x^2 + y^2 = 4b$$ and $$\frac{x^2}{16} + \frac{y^2}{b^2} = 1$$ lie on the curve $$y^2 = 3x^2$$, then $$3\sqrt{3}$$ times the area of the rectangle formed by the intersection points is _______.
Correct Answer: 432
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