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 $\_\_\_\_$.