Let a line L: 2 x+y= k, k >0 be a tangent to the hyperbola x^2-y^2=3. If L is also a tangent to the parabola y^2=α x, then α is equal to:

Let a line $\displaystyle \mathrm{L}: 2 x+y=\mathrm{k}, \mathrm{k}>0$ be a tangent to the hyperbola $\displaystyle x^2-y^2=3$. If L is also a tangent to the parabola $\displaystyle y^2=\alpha x$, then $\displaystyle \alpha$ is equal to :