Ok there is a new Supergirl TV show on the way, but someone has their information a little wrong.
Either they are changing it or someone has not done their homework. Kara aka Supergirl is the cousin of Kal-el aka superman. In the family of El there were two brothers, Jor-el and Zor-el. Zor-el lived in Argo city. When krypton exploded Argo city survived, that because there was a protective dome that covered the city. Argo city floated in space for many years and upon the explosion the ground turned to kryptonite. They used lead shielding that the scientists rolled out and protected them from radiation. Many years later Zor-el and his wife had a baby Kara and many years after Krypton explodes, Kara was in her early teens when her father, Zor-el foresaw a meteor storm heading towards the dome. Knowing all its inhabitants were doomed, he sends Kara to earth in a rocket, so she would survive and be with her cousin, there she become Supergirl.