My children are young so I cannot go to the mosque for Taraweeh prayers but I really want to listen of Qur'an. Is it correct to perform Taraweeh following the Imam of Makkah on TV?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is not permissible to be led by an Imam through a radio or a TV set when performing the prayer, whether Taraweeh prayer or other prayers.

The questioner could perform Taraweeh prayer at home by what she memorizes of short or long Surah (chapters) from the Qur'an.

It is better for optional prayers to be performed at home, and among these optional prayers is Taraweeh.  The Prophet (Sallallahu Alaihi wa Sallam) said: "Perform some of your prayers at home and do not make your homes graves." [Reported by Bukhari and Muslim]

The Prophet (Sallallahu Alaihi wa Sallam) further said: "The best of your prayers is the one performed at home except the obligatory one."

The Prophet (Sallallahu Alaihi wa Sallam) said regarding women: "Do not prohibit your women from going to the mosque, but their homes are better for them." [Reported by Abu Dawud]

Allah knows best.