I don't know much about Mayuka except that she's technically Tenchi's daughter although Yazuha (Mayuka's mom) and Tenchi didn't have sex . . .

Well, here it goes, Yazuha came to acquire a lock of Tenchi's hair. Yazuha took the DNA from Tenchi's hair and combined it into her ovum, hence Mayuka is created.

Mayuka is in the Tenchi Muyo movie: daughter of darkness.