Blood test

How far along do you have to be to get a positive blood test from the doctor? Could it be possible to get a negative test and still be pregnant? I missed my period this month it was due on the 3rd but I had sex only on the 30th. I got my blood taken on the 10th and it was negative but still no period. I only received spotting the beginning of the month that stopped... I stopped birth control pill in June and this is the first time my period hasn’t come.