$\mathrm{O}(0,0)$ and $\mathrm{A}(1,0)$ are centres of two unit circles $\mathrm{C}_1$ and $\mathrm{C}_2$ respectively. $\mathrm{C}_3$ is also a unit circle having its centre above $\mathrm{X}$-axis and passing through $\mathrm{O}$ and $\mathrm{A}$. The equation of the common tangent to $\mathrm{C}_1$ and $\mathrm{C}_3$ which does not intersect the circle $\mathrm{C}_2$ is