The officer likely didn't have enough to get you on speeding - even when they do, police hate to fight tickets and thus they'll try to the driver to admit to doing something wrong ... basically what the officer did in your situation - by the textbook

You should tell your parents, because quite honesty, it sounds as if the traffic stop and ticket are both bogus - if you can fight the ticket, seriously consider doing so.

On a related note, officers typically have to follow closely behind for 1/4 mile to write a ticket for speeding - and in most states, the driver is legally given a decent amount of leeway in exceeding the speed limit when being followed (unless the driver admits speeding) ... most often the officer won't even write a ticket for speeding in such a situation unless the driver admits doing so - reason is that in court, such a ticket is relateively easy to challenge, such as questioning how long the officer was following behind, was it a consistant distance, and was the vehicle's speedometer is certified among other things, etc.

Good luck...

Ron