You have |z + 24| = 3|z - 8i|. The locus is a Circle of Apollonius.

With a bit of effort you can re-arrange the given relation into the form |z - a| = r and hence recognise it as a circle with radius r and centre at z = a. However, I recommend the Cartesian approach of substituting z = x + iy as being more efficient.

I haven't checked your answer (except to check that you get a circle, which you did) - I assume if you can do basic algebra you will get the correct answer.