Explanation:

- Kathak is a classical dance form that originated in North India. It is particularly associated with Uttar Pradesh, where it flourished in royal courts.

- Option 2: Uttar Pradesh - Kathak is deeply rooted in the culture of Uttar Pradesh. It evolved in the temples and later found patronage in the Mughal courts.

- Option 1: Tamil Nadu - Tamil Nadu is famously known for the Bharatanatyam dance form, not Kathak.

- Option 3: Manipur - This northeastern state is known for the Manipuri dance style.

- Option 4: Assam - Assam is renowned for its dance form called Sattriya, not Kathak.