As a rule of thumb, you will be considered a citizen of a country if you were born there and your parents were also citizens. Additionally, many countries extend the right to citizenship even to descendants of citizens who had left the country.
Depending on your ancestral country, you can usually become an EU citizen if your parents were citizens. In some cases, even your grandparents or great-grandparents may be considered, or any ancestors back to the foundation of the country – you can find an interactive map with the number of relevant generations here. (Mind you, because of the history of Europe, in some cases “the foundation of the country” as it is today means only the 20th century, or the second half of the 19th century.)
In this sense, Hungary is among the EU countries with the most favorable conditions for obtaining citizenship by descent. There is no restriction on the number of generations, and there is no specific date before which your family will not qualify. You just need to show a paper trail of your ancestors.