The Gem says that he R' Elazar ben Azaryah learns out from Makas Bechoros that just like that was Ad Chatzos so too we can eat the korbon Pesach ad Chatzos .
*Ad Chatzos* is not the same as Kechatzos ; so why doesn't he require one to eat Matzo/Korban Pesach at midnight as the Posuk really says?!
Kol Tuv
alex lebovits, toronto, canada
The Madanei Yom Tov in Berachos (9a, note Alef) seems to be bothered by your question. He explains that the Mitzvah cannot possibly be to eat the Pesach exactly at Chatzos, as they wouldn't know the exact instant and it takes longer than an instant to eat. It can't be after Chatzos, as the point of the Pesach was to protect them from Makas Bechoros. Therefore, being that the Pasuk writes the same terminology by both, it clearly wants us to learn that we should eat the Pesach before Chatzos as did Bnei Yisrael.
All the best,
Yaakov Montrose