Poorly written English - Needs to be revised.
The Carnatic coast /kɑːrˈnætᵻk/ is the region of South India lying between the Eastern Ghats and the Coromandel Coast, in the modern Indian states of Tamil Nadu, south eastern Karnataka, north eastern Kerala and southern Andhra Pradesh.
The name 'Carnatic' or 'Karnatic' is originally a Tamil word which means that 'Karai'(கரை) meaning 'shore' 'nataka'(நாடக) meaning dance. Since the word 'Carnatic' or 'Karnataka' region and music or 'கரை நாடக சங்கீதம் (Tamil)' is the base of Kaveri-based regions during the chola periods (especially developed in the city of Poompuhar (பூம்புகார் ), which was swallowed during a tsunami - remains still can be seen in Tamil Nadu with the same city name) to improve and to integrate Tamil based dance and music. So comes the name 'carnatic' or 'Karnatic' region / zone, as big landscape covering the whole gamut of kaveri based areas in Tamil Nadu, Karnataka, Kerala and some in Andhrapradesh. This particular dialect has been introduced during the Chola time period as a proof of in 'Carnatic' or 'Karnatic' zone development. In a later stage, this was combined together with Sanskrit words due to the acceptance of 'Hinduism' by Chola and later 'Pandyan' kings. The base of the underlying music is Tamil based only. Even though there has been many changes during the period of 'Rashtrakutas' and later 'Vijayanagar' kings.
Further to add, there are several theories as to the derivation of the term. It may derive from the Sanskrit language karņāţakam from karņa = "ear" + aţati = "he pleases" = "that which pleases the ear", thus "Karnāṭaka saṃgīta" = "Karnataka music", which was coined by Sarangadeva.