You are "servient" and the city is "dominant" when it comes to easements. You get to enjoy the property (Look at but not build upon, keep up the property (ie" mow & weed.) and use the property (ie: stand on.). The city retains rights to the property and everything underneath. Most cities have an easement behind property to erect power/telephone/cable poles or in your case bury drainage pipes.
Easements can very from a few feet on both sides of the property line to 10 sometime 15 feet on both sides. You can go to your counties GIS and look up your property. Doing a plot map version instead of a the Google Earth (picture) version. This usually has the easement on it.
If you do have an easement, then yes, you're screwed.