The son of a merchant from Ryazan, he taught himself how to paint from a young age.
In 1826, he presented his work to Grand Duke Michael Pavlovich of Russia, who accepted the young man under her patronage and entered him into the St. Petersburg Academy of Fine Arts.
After obtaining two silver medals, Zhivago finished his formation and soon left for his own calculation, into Italy, where he painted copies of famous Italian paintings for a living.
For these works, on his return to Saint Petersburg, in 1839, it was acknowledged as an academician.
From 1848 through 1850, he served with the Petersburg custom-house as expert for the painting recognition.