Translation:My father is young, but my grandfather is old.
"A" does not have a unique analogue in English. In sentences like this, it's quite analogous to English "whereas", but Duo finds "whereas" too highbrow and relplaces it with "ands" and "buts" as it sees fit.
Another common use of Russian "a" is in sentences where the first part contains negation: "он не молодой, а старый", and in this case the best English match would be "but rather" or "but ... instead".
One of these days - or maybe not - I suppose there might be some instruction or even discussion by Duo about formation of adjective endings. So far, no such luck.
From what I've read so far, -ый is only used with "hard-stemmed adjectives" (whatever that means). -ой is used with hard-stemmed adjectives, with stem ending in -г, -к, -х, -ж, -ш, -ч, -щ (which call also end in -ий).
Adjectives remain a great mystery with only a part of their construction rules revealed. So far.
Here is the pattern for известный, which is hard-stem stem-stressed adjective with no quirks
You can compare it to какой, which is ending-stressed and has a К before the ending. See how well you can predict how to "fix" the ending of известный to get the correct one.
Russian has palatalised ("soft") consonants, like in пять, and non-palatalised ("hard") consonants, like in мотор. This is where the names come from.
Russian adjectives fall into roughly four categories with minor difference in endings.
- like зелёный ("hard stemmed")
- like синий ("soft stemmed")
- like тихий (к-г-х stem)
- like старший (ш-ж-щ-ч stem)
Hard-stem adjectives use endings like зелёный, зелёного, зелёном, зелёным, зелёное, зелёная, зелёной, зелёные etc.
Soft-stem adjectives use endings like in синий, синего, синем, синим, синее, синяя, синей, синие etc.
The adjectives with к,г,х, щ,ч,ш,ж and ц before the ending will use the combination of the two depending on what is known as "spelling rules" by Russian learners.
ОЙ is the masculine Nominative ending for ending-stressed adjectives (e.g., большой, святой). Full adjectives have a fixed stress in Russian, so once you know the word the stress is always either on a syllable of the stem or on the ending, with no unexpected shifts somewhere else.
Possessive adjectives form a sub-group within Russian -ий-ending adjectives. Everywhere except in the base form, A ь is put before the ending, and if there are two consequtive vowels, the first gets removed. For some reason, третий ("third") follows this exact pattern (третий, третьего, третья, третье, третьих).
- effectively, you get a Y-sound at the start of most endings, which absorbs the following vowel when followed by two of them.