Taking the origin as the intersection of $a$ and $b$, with the equation in terms of the angle $\theta$ at that vertex:
Through the cosine law we have:
With our particular setup, $a$ is the radius. So this is a polar equation, where
we can convert to cartesian coordinates if you want:
which is a hyperbola. You want the rightmost branch (so $a>0$), which is valid when $\cos\theta<\frac 1 5$.
EDIT: picture time!