"I've already told one or both of them, whether or not they accepted it."
"Only if they think it's relevant to their relationship or to the conversation."
I told my mom a few weeks after I discovered asexuality myself. I've learned through experience that everything I tell my mom eventually gets told to my dad, so I assumed that he knew already a little while after that. I've also mentioned it off-hand in a few conversations since then ... my whole immediate family knows now. I just like it better that way. I don't feel like I have to hide anything.
I could have probably gotten away with not telling any of them, since I do tend to date normally, and what does or doesn't go on in the bedroom remains
my business and mine alone. However, someone who is aromantic may choose to divulge the information that they're asexual to get their parents off their backs about not dating. For example, I recently came into a period of my life where I don't want to date anymore, and I'm thinking that may mean I have to tell more people that I'm asexual just so that I don't have to deal with people insisting I should try dating again.
The situation is going to be different for each individual of course.
"Love / so much to give / and so few to share it with / wastes you away" ~Oceansize