megusuri wo tukue no ue ni oita mama dekakeru tokorodatta.

〜たまま means leaving something in the state it ended up in, or without changing that state.

So:

• 置いたまま = left it placed there
• more literally: with it having been placed there, and still in that state

In this sentence, it means the eye drops were left on the desk, and that situation was still unchanged when the speaker was about to go out.

A natural English way to think of it is:

• leaving the eye drops on the desk
• with the eye drops still sitting on the desk
• without putting the eye drops away

This is a standard grammar pattern:

• verb in past/plain form + まま

So you get:

• 開けたまま = leaving it open
• 座ったまま = remaining seated
• 置いたまま = leaving it placed there

The past form here does not mean ordinary past tense in the English sense. In this pattern, 〜た shows that the action has been completed, and then the resulting state continues.

So:

• 置いた = placed it
• 置いたまま = placed it and left it like that

That is why 置くまま would not work here.

〜ところだった often means was just about to do or almost did.

Here:

• 出かける = to go out / leave
• 出かけるところだった = was just about to go out

So the sentence means the speaker was at the point right before leaving.

This pattern is:

• dictionary form + ところだ = be just about to do
• dictionary form + ところだった = was just about to do

The past だった is used because the speaker is looking back on that moment.

Because the form before ところ changes the meaning.

• 出かけるところだった = was just about to go out
• 出かけたところだった = had just gone out
• 出かけているところだった = was in the middle of going out / was just leaving

So in your sentence, the speaker had not left yet. They were on the verge of leaving.

That is why 出かけるところだった is the correct form.

Because 置く is a transitive verb, and the thing being placed is its direct object.

• 目薬を置く = place the eye drops
• 本を置く = place a book
• かばんを置く = put down a bag

So 目薬を tells you what was being left on the desk.

Even though English might focus more on the location, Japanese still treats the thing being placed as the object of 置く.

Also, 目薬 here refers to eye drops as an item, often basically the bottle/container.

Because に is commonly used with verbs of placement to mark the place where something ends up.

• 机の上に置く = put it on the desk
• 箱に入れる = put it in the box
• 壁に掛ける = hang it on the wall

Here, に marks the destination/location of placement.

By contrast, で usually marks the place where an action happens.

For example:

• 机の上で勉強する = study at the desk
• 部屋で食べる = eat in the room

So:

• 置く focuses on where the object is placed → に
• 勉強する / 食べる / 話す happen at a place → often で

It literally means the top of the desk.

Breakdown:

• 机 = desk
• の = of
• 上 = top / above / on top

So:

• 机の上 = the desk’s top surface
• natural English: on the desk

Then adding に gives:

• 机の上に = on the desk

Yes, the subject is omitted, which is very normal in Japanese.

The sentence does not explicitly say I, he, she, etc. The subject is understood from context.

Most naturally, this sentence would often mean:

• I was about to go out, leaving my eye drops on the desk.

But depending on context, it could also refer to someone else:

• He was about to go out leaving the eye drops on the desk.

Japanese often leaves out information that is already understood, especially subjects and topics.

A useful breakdown is:

• 目薬を = the eye drops
• 机の上に = on the desk
• 置いたまま = leaving them there / with them left there
• 出かけるところだった = was just about to go out

So the structure is roughly:

[object] + [place] + [left in that state] + [was just about to go out]

A very literal rendering would be:

• I was at the point of going out with the eye drops left on the desk.

A more natural English version would be:

• I was just about to go out leaving the eye drops on the desk.
• I almost went out with my eye drops still on the desk.

Usually, yes — or at least that the speaker noticed it as something important.

〜たまま often carries the nuance of leaving something as it is, sometimes when that is unintended, careless, or undesirable.

So this sentence often suggests something like:

• I almost went out without taking care of the eye drops.
• I nearly left while my eye drops were still sitting on the desk.

The sentence itself does not explicitly say that was bad, but in normal context it strongly suggests the speaker realized it just in time or thought, Oops, I was about to leave them there.

Because Japanese does not need to state the topic every time, especially if it is already obvious.

For example, a fuller version might be something like:

• 私は、目薬を机の上に置いたまま出かけるところだった。

But once the topic is understood, Japanese often drops 私は.

So the sentence without は sounds natural and not incomplete. It simply presents the event directly.

Yes, in casual speech you might hear something like:

• 目薬を机の上に置きっぱなしで出かけるところだった。

置きっぱなし means leave something as it is, often with a stronger feeling of just leaving it there carelessly.

Difference in nuance:

• 置いたまま = neutral, grammatical, standard
• 置きっぱなし = more casual, often sounds more careless or neglectful

So both can be similar, but 置いたまま is the more straightforward expression in your sentence.