たところ details

write + (past) + I did X, and this is what came of it

kaita tokoro

I did X, and this is what came of it

meaning: upon writing

店みせに問い合わせといあわせたところ、在庫ざいこはもうないと言いわれた。

mise ni toiawaseta tokoro, zaiko wa mou nai to iwareta.

I was told there was none left in stock upon enquiring at the shop. neutral

薬くすりを飲のんだところ、熱ねつはすぐに下さがった。

kusuri o nonda tokoro, netsu wa sugu ni sagatta.

I took the medicine, and the fever came down right away. neutral

Examples

I did X and found out Y — the speaker takes a step (asking, checking, trying) and reports what it turned up

店みせに問とい合あわせたところ、在庫ざいこはもうないと言いわれた。

mise ni toiawasetatokoro, zaiko wa mou nai to iwareta.

I was told there was none left in stock upon enquiring at the shop. neutral

薬くすりを飲のんだところ、熱ねつはすぐに下さがった。

kusuri o nonda tokoro, netsu wa sugu ni sagatta.

I took the medicine, and the fever came down right away. neutral

何通なんとおりか試ためしたところ、この方法ほうほうが一番いちばん速はやかった。

nantoori ka tameshita tokoro, kono houhou ga ichiban hayakatta.

I tried it several ways, and this one turned out fastest. neutral

先方せんぽうに確認かくにんいたしましたところ、日程にっていの変更へんこうは可能かのうとのことでございます。

senpou ni kakunin itashimashita tokoro, nittei no henkou wa kanou to no koto de gozaimasu.

I checked with them, and it appears the schedule can be changed. formal

たところが — が added where the finding goes against what the speaker expected — 早はやめに着ついたところが、店みせはまだ開あいていなかった。
ましたところ — the ました form carries into the clause in business writing — 担当者たんとうしゃに確たしかめましたところ、手続てつづきは完了かんりょうしておりました。

たら
たら only supposes the act, so it chains onto anything at all, a request or a plan included (着ついたら電話でんわして); たところ says the act really happened and hands over what it turned up, so ×問とい合あわせたところ、また連絡れんらくしてください is out where the たら version is ordinary.

ところだ
One だ decides it — 聞きいたところだ ends the sentence and claims the asking happened moments ago, while 聞きいたところ、 breaks off at a comma with the answer still to come and makes no claim about how recent it was.
たところで
One kana apart and opposite about whether the act happened — たところで supposes one that has not and writes it off (聞きいたところで無駄むだだ), たところ reports one that did and hands over what it turned up (聞きいたところ、教おしえてくれた).