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 ∈(0, ∞) of the tangent to the…

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