Final answer:
The Muslim rulers founded their capital at Delhi, notably under the Delhi Sultanate and later the Mughal Empire, with Emperor Shah Jahan moving the capital back to Delhi in 1648.
Step-by-step explanation:
The Muslim rulers of India founded their capital at Delhi. Over its history, India saw various seats of power depending on who ruled at the time. In the twelfth century, Muhammad of Ghur established what would become known as the Delhi Sultanate, choosing Delhi as the administrative heart of his newly conquered territories. This Muslim state endured for more than three centuries.
The Mughal Empire, another significant Islamic empire, also designated Delhi as its capital, except for some brief periods. Notably, in 1648, Emperor Shah Jahan, renowned for commissioning the Taj Mahal, moved the Mughal capital from Agra back to Delhi, where he initiated the construction of famous buildings such as the Red Fort.