Get lat lon for a pos when only dx dy is known from an other point

The problem I have is getting the latitude and longitude for a position when I know one origin position and the offset to the other point (in meter)

I want to use following function (or any other function that gives me a correct lat2 and lon2):

import geographiclib
geographiclib.geodesic.Geodesic.Direct(self, lat1, lon1, azi1, s12)

I have some example data:

lon1 = 11.62113333
lat1 = 55.9862

dx = -51659.25 #meter
dy = -33702.33 #meter

This is the result that I'm hoping to achieve:

azi1 = -120.95109978727244
s12 = 61691.57175978693         
lat2 = 55.69834 
lon2 = 10.77969

When I use a UTM2latlon converter I'm getting a position that is way off.. I think that the coordinate system that is used to calculate dx and dy is ESPG:5596.

Since the distances is great and the distance have taken into account for the earthsPythagoras Theorem isn't applicable to calculate s12 and azi1. Any suggestions on functions etc.?

Solution

Thanks for the try!

Unfortunately I worked with some old algorithm so the "correct answer" was a more trivial function.

def melat(lat):
    return  degrees( log ( tan ( radians( lat / 2 + 45 ) ) ))

def latit(mlt):
    return ( degrees(atan ( exp ( radians(mlt) ) )) - 45 ) * 2

def XY2LatLong(x, y):
    EQUATOR_MINUTE_LENGTH = 1851.8518519
    GeoPoint = namedtuple('GeoPoint', ('lat', 'lon'))
    Point = namedtuple('Point', ('x', 'y'))
    base = GeoPoint(55.98619572, 11.62113936)
    factor = cos( radians(base.lat) ) * EQUATOR_MINUTE_LENGTH * 60.
    return GeoPoint(
        latit(melat(base.lat) + y / factor),
        base.lon + x / factor)