Step 1: Understanding the flow of Yamuna River.
The Yamuna is the second-largest tributary of the Ganges and flows through several cities in northern India including Delhi, Mathura, and Agra.
Step 2: Identifying the correct city.
Agra is directly located on the banks of the Yamuna and is home to the Taj Mahal, which also sits beside the river.
Patna and Varanasi are located along the Ganges River, not Yamuna.
Haridwar is also on the Ganges.
Step 3: Elimination.
Thus, only Agra fits the requirement correctly.