Let \( y^{2}=12x \) be the parabola and \( S \) be its focus. Let \( PQ \) be a focal chord of the parabola such that \( (SP)(SQ)=\dfrac{147}{4} \). Let \( C \) be the circle described taking \( PQ \) as diameter. If the equation of a circle \( C \) is \( 64x^{2}+64y^{2}-\alpha x-64\sqrt{3}\,y=\beta \), then \( \beta-\alpha \) is equal to _______.
