how to remove broken key from door lock (Miata)

Hello!
   Removing a broken key from a door lock cylinder is not always possible; it depends on how deep into the lock the key is broken off, whether the broken key is twisted and jammed into place, and whether there is any internal damage to the lock such as bent wafers that are wedging the broken key in place.
   Locksmiths use a special tool that looks like a piece of wire with a sharp barb on the end to reach into the lock opening to attempt to pull the broken key out.    usually these tools are only available by special ordering them from a locksmith supply company; they are not something you can usually buy over the counter anywhere.    If you want to try something, you may be able to make a similiar type of tool by buying a medium sized fishing hook from your local sporting goods store (less than a dollar) and see if you can straignten it out enough to be able to insert it into the lock.
   If you cannot get the broken key out, the only repair is to order a new lock cylinder from your local mazda dealer.   The dealer can code the new lock to match your existing key code (they can look this up in their dealer computer system using your VIN number).