Hyperbola

Let the equation of two diameters of a circle \(x^{2}+y^{2}-2 x+2 f y+1=0\) be \(2 p x-y=1\) and \(2 x+p y=4 p\). Then the slope m \(\in\) \((0, \infty)\) of the tangent to the hyperbola \(3 x^{2}-y^{2}=3\) passing through the centre of the circle is equal to _______________.