Cars manufactured in and after April 2010 had a LSD. I.e. the last production run.
If you wheelspun with a LSD it would leave two black lines. That's the point of it. When one wheel starts spinning, due to its mechanicals it sends power down both driveshafts. That's why you corner better.
With an open diff it sends power to the wheel that is easiest to turn, which is the wheel that is already spinning.
Dealer will be able to tell you probably from the reg, but definitely the VIN. They need to be able to tell on the parts system when you have, say for example your gearbox breaks, so they can order the right parts for replacements.
To be honest, if it was registered in April I doubt it.