See: List of castles, Castles in England, Castles in Scotland, Castles in Northern Ireland
Anglesey
Clwyd
Dyfed
Glamorgan
Gwent
Gwynedd
Powys
South Glamorgan
West Glamorgan
... of the form x2 + 2xy + y2. Since "2xy" in this case is (b/a)x, we must have y = b/(2a), so we add the square of b/(2a) to both sides, ...