Slope of the Other Tangent Line to a Circle

From the point $(2,5)$, the slope of one of its tangent lines to a circle with center at $(0,0)$ is $2$. What is the slope of the other tangent line from $(2,5)$ to the same circle? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.