From a famous poem in English by Samuel Taylor Coleridge. He was reading about this place when he fell asleep and dreamed a strange dream. He woke up and wrote a long poem. He was taking opium (as medicine) at the time, so that may explain why his dream was so bizarre!
It seems that he was reading a translation of Marco Polo's book in which Shangdu, the site of Khubilai Khan's summer palace, was spelled as 'Xandu.' Then he took some liberties with the spelling.
We don’t know for sure if he actually got to Xanadu. A lot of people think he did because he described it in great detail. In fact, his is the only description we have of Xanadu.
Actually this is an old name for the city now known as Beijing. In the ancient days, it was a small city called Yanjing and later Zhongdu. That city was burned to the ground by Chinggis Khan in 1215. Fifty years later, Khubilai Khan decided to build a magnificent palace and a grand capital with thick walls and broad avenues just across the river from the old town; he called the city ‘Khanbalik,’ which means ‘Khan’s capital’ in Mongolian. In those days, the Chinese name for this city was ‘Yuan Dadu,’ or Great Capital of the Yuan Dynasty. Marco Polo heard the name Khanbalik and spelled it ‘Cambaluc,’ which is a very romantic medieval name for the city. When the Chinese took back control, they called it ‘Northern Capital,’ which is pronounced ‘Beijing’ in Chinese. They destroyed the Khan’s great palace and built an even bigger one of the same site; you can see it today as the Forbidden City or the Imperial Palace, one of the most famous sites in Beijing. The French called the city Pekin, and the English called it Peking. Today, the Chinese government spells the name ‘Beijing,’ and it is the capital of the People’s Republic of China. The Olympics were held there in 2008, not far from where Emmajin used to ride her horse.
Yes, it seems highly likely he did. From the day he got back home, people thought Marco Polo was exaggerating or lying about the fabulous wealth and wonder of the empire he claimed to have visited. In those days, Venice was the most powerful, prosperous city in Europe, and Venetians did not want to believe there was a land that was far more advanced. In fact, they called Marco “Il Milione” because he claimed to have seen “millions and millions” of jewels, people, soldiers, everything. About 50 years after his book came out, an extremely popular travel book appeared, by “John Mandeville,” about a journey to the Orient. It was lively and fun to read, and told of terrific monsters, dog-headed cannibals, people with ears hanging to their knees, and men whose heads grow beneath their shoulders. It later proved to be mostly invented or borrowed from other writers, so that made people wonder about the truth of Marco Polo’s book, too. For hundreds of years, Europeans could not travel safely to the Far East, so they had no way of checking. However, when Europeans began to explore Asia, they found that most of Marco Polo’s descriptions of remote places were remarkably accurate. Many Europeans did travel to China during the relatively peaceful years of the Mongol Empire, both traders and priests, so it is not hard to believe that one of them wrote a book about his travels when he got home.
For a scholar's explanation of these misunderstanding and misinterpretations, see "F. Wood's Did Marco Polo Go To China? A Critical Appraisal" by I. de Rachewiltz.
The Complete Yule-Cordier edition of The Travels of Marco Polo also refutes these doubts, on pages 109 - 166, as does Professor John Warner on pages 60 - 63 of Marco Polo and the Discovery of the World.