Grammar for verb + ところ:
plain non-past verb + ところ = just about to do...
~ている+ ところ = am currently doing
~た+ ところ = have just done
Taberu tokoro desu.
I'm about to eat.
Tabete iru tokoro desu.
I am still eating.
Tabeta tokoro desu.
I have just eaten.
~た+ところ can be replaced by ~た+ ばかり to indicate what you have just done. However, ところ is more immediate and definite, while ばかり means "recently" (instead of "just a while ago") and thus gives a more personal meaning as to what "recently" means.
This blog entry gives a nice example. Suppose you saw a woman who has a wedding ring, and you think she just got married.
Kekkon shita bakari mitai desu.
She looks like she just got married.
You can't use ところ here because it wasn't like the woman got married minutes ago.
On the other hand, you say:
Kuukou ni tsuita tokoro desu.
I've just arrived at the airport.
It means you have literally just arrived at the airport.