Calender shows two times generally...
1st. Stop Eating time
2nd. Fajr Adhaan time
It is ok to eat until the Adhaan of Fajr... and couple of minutes after Fajr if the food in your plate which you intended to eat is not finished... so it is not wasted.
But this does not mean that you can keep eating 5-10 mins after adhaan.
So, if you ate the food well after the time of Fajr Adhaan...then your fast is not valid.
However, you still cannot or should not eat or drink anything until the time of Iftar. In addition, you'll have to make up the fast you missed.
Note: It is ok to fast without suhur if you happened to miss it. It is sunnah to eat before the Fajr Adhaan but eating after it nulifies ur fast.
Also, missing suhur consistantly is not allowed either, because the jews fast from night before till the night of the next day... and the Prophet (sws) commanded us to not be like the Jews and the Christians.
Allah knows best.
W'salaamz,
Hamid