You are correct. Beowulf's father was indeed Ecgtheow, and his mother was the daughter of Hrethel, king of the Geats. Beowulf introduces himself as the son of Ecgtheow in Chapter IV:
My father was known to far-off folk: Ecgtheow was his name. A man of many winters, he departed as an aged man from the earth and is honored even today by sage men throughout the world's width.
When Hrothgar hears that Beowulf has arrived, he remembers him as the son of Ecgtheow and an unnamed daughter of Hrethel:
...his aged father was named Ecgtheow, to whom Hrethel the Geat gave his only daughter.
Later Hrothgar describes a bit of Ecgtheow's history, telling Beowulf that his father had kindled a blood-feud by killing one "Heatholoaf of the Wylfings," and that he had been given shelter among the Danes. Hrothgar even settled the feud for Ecgtheow, and Beowulf's father swore fealty to him in return. So Ecgtheow is, definitively, Beowulf's father. Hygelac, incidentally, was a son of Hrethel, the Geatish king who raised Beowulf. He would have been Beowulf's uncle on his mother's side, not his father.
On arrival at the Danish sea shore, a warrior of the Danes asked Beowulf and his team to state their origin and purpose for visiting their lands. Beowulf responded by stating that they were from the Geats’ clan under the leadership of Hygelac. Beowulf further stated that his father was well known and respected, and he went by the name of Ecgtheow. Thus, Ecgtheow was Beowulf's father, and your answer was correct.
Hrothgar, the King of the Scyldings, stated that he knew Beowulf when he was younger. He further stated that Beowulf’s father was named Ecgtheow and his mother was the only daughter of Hrethel. Hrothgar told Beowulf of how his father started a blood feud with the Wylfings after he murdered their kinsman. Hrothgar added that he was responsible for Ecgtheow’s safety and the end of the feud after he settled the blood price.
HROTHGAR, THE CROWN of the Scyldings, spoke: “I knew him from his young days; his aged father was named Ecgtheow, to whom Hrethel the Geat gave his only daughter.