How can I convince my parents that my future is secure in the performing arts?

I come from a well educated family. My father is a business architect, my mum a qualified nurse and my brother is going to medical school to study anesthesia. Despite this, my heart is set on going to a performing arts academy. My parents are unconvinced, however they do pay for me to partake in a youth theatre academy and ure me that I have a brilliant talent for performing and a great stage presence. How can I convince them that acting and theatre is my future and the only career I will be truly happy in?