Diagnose DNS problem

[Colin Law]

I have an Ubuntu 18.04 system at a relative's home that has a DNS
issue that I don't know how to diagnose.  When I run, for a particular
domain

ping a.domain.com

I get
ping: a.domain.com : Name or service not known
but when I run ping with the actual IP address it is ok, and if I run
it (using the name) from any other location it works fine.  I assume
that means that I have a DNS problem with that machine or network.
DNS seems to work ok on all other domains that I have tried.  I don't
know how to diagnose this, so any suggestions will be gratefully
received.

Colin