A póráz az ajtónál van.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

So:

• a póráz = the leash
• az ajtónál = at the door

They mean the same thing as English the; the choice just depends on pronunciation.

Ajtónál is built from:

• ajtó = door
• -nál = a suffix meaning at / by / near

So ajtónál literally means at the door or by the door.

This is very normal in Hungarian: instead of using a separate preposition like English at, Hungarian often adds a suffix to the noun.

The ending -nál / -nél is the adessive ending. It expresses the idea of being at, by, or near something.

It appears here as -nál because ajtó has back vowels, so it takes the back-vowel version of the suffix.

Compare:

• ajtónál = at the door
• széknél = at the chair

This is part of Hungarian vowel harmony.

That is a very common question.

In Hungarian, van is often omitted in the present tense, third person, when you are saying that something is something:

• A póráz új. = The leash is new.
• A póráz hosszú. = The leash is long.

But when you say where something is, Hungarian normally keeps van:

• A póráz az ajtónál van. = The leash is at the door.

So in this sentence, van is needed because the sentence gives a location.

Because it is the subject of the sentence, and Hungarian subjects are usually in the nominative, which typically has no ending.

So:

• póráz = leash
• a póráz = the leash

If the word were an object instead, it would usually get a different ending, such as -t:

• Látom a pórázt. = I see the leash.

Yes. Hungarian word order is flexible, and changing it often changes the focus or emphasis.

The given sentence:

• A póráz az ajtónál van.

is a natural neutral way to say The leash is at the door.

But you could also say:

• Az ajtónál van a póráz.

This puts more emphasis on the location, as if answering Where is the leash?

So the meaning stays close, but the information structure changes.

Because these mean different things:

• ajtónál = at/by the door
• ajtón = on the door

So if the leash is lying next to the door, you use ajtónál.

If the leash is hanging on the surface of the door, you would use ajtón:

• A póráz az ajtón van. = The leash is on the door.

This is an important distinction.

A few helpful points:

• Hungarian stress is almost always on the first syllable
• Accent marks usually show vowel length
• pronunciation is quite regular

So:

• póráz is stressed on pó-
• ajtónál is stressed on aj-

Also:

• aj sounds roughly like English eye
• ó and á are long vowels

So ajtónál sounds approximately like EYE-toe-naal, with the stress at the beginning.

Because az ajtónál is a full noun phrase meaning at the door.

Hungarian often uses the article with specific nouns in these location phrases, just as English does in this sentence:

• at the door
• by the door

So az belongs with ajtónál and means the. The sentence literally has:

• A póráz = The leash
• az ajtónál = at the door
• van = is