AIEEE 2002 (Offline)Question 1
The locus of the centre of a circle which touches the circle $|z-z_1|=a$ and $|z-z_2|=b$ externally ($z,z_1\ \&\ z_2$ are complex numbers) will be :
Complex Numbers
Solution
If the circle has centre $P$, radius $r$: $|P-z_1|=r+a$, $|P-z_2|=r+b$, so $|P-z_1|-|P-z_2|=a-b$ is constant: a (branch of a) hyperbola.