Im a vegan and everyone thinks i never eat?

so i just switched from being a vegetarian to a vegan. almost everyone in my family seems to be convinced that i dont eat. my mom thinks i dont eat but instead of just asking me if im eating she gets mad at me and is like "why havent u been eating!? dont start this again." and what she means by dont start this again is that i used to be anerexic and bulimic BUT IM NOT ANYMOREE and she doesnt trust me.noone trust me anymore cuz they always think i still have anerexia or bulimia when i DONT AND I DONT WANT TO HAVE THEM ANYMORE! im a vegan cuz i LOVE ANIMALS and ive seen many videos about what happens in slaughterhouses and i dont want anything to do with dairy or meat anymore. but the thing is..I DO EAT! i just rlly healthy food liek fruits and vegtables and stuff. and plus i run 3 miles everyday and play tennis so im active, and i dont drink sodas except like once a week ill have a diet one, i only drink water, green tea, and redbull. so when i loose wieght or look slimmer its cuz im so active. and i DO eat. i eat a big breakfast usually consisting of 2 big bowls of cherrios with flaxseed dairy-free milk. for lunch ill have like some sort of steamed veggies. and dinner ill wat whatever i can find thats vegan. and for snacks i have pretzals or carrots with vegan hummus and organic salsa. how can i convince my mom and family that even though i am a vegan i stilllllll eatttt and im not anerexic or bulimic anymore? nor do i plan on going down that path again. thx ill give best answer!