The locus of the centre of a circle which touches the circle | z – z1 | = a and | – 2 | = b externally (z, z 1 & z 2 are complex numbers) will be

The locus of the centre of a circle which touches the circle $\left|z-z_{1}\right|=a$ and $\left|\mathrm{z}-\mathrm{z}_{2}\right|=b$ externally $\left(z, z_{1} \& z_{2}\right.$ are complex numbers) will be