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