How do amendments ix and x apply to the constitutional principles of separation of powers and balance between government authority and individual rights?

Amendment 9 -- rights defined here don't mean other rights aren't for real. Amendment 10 -- Rights not delegated to the federal government by the constitution, and not denied to the states by the feds explicitly, are reserved to the states or to the people themselves. If the feds don't define it, go for it. The ninth and tenth amendments represent the end product of a feud between the Federalists and Anti-Federalist camps at the Constitutional Convention, which is still seeing heat today, usually with Roman candle terms such as "expansion of powers," "Big Government," "States' Rights" and so on.

The answer is

In 911, a group of vikings lead by rollo besieged paris and chartres. after a victory near chartres on 26 august, charles decided to negotiate with rollo. the talks were led by hervé, the archbishop of reims. this resulted in the treaty of saint-clair-sur-epte, which granted rollo and his soldiers all the land between the river epte and the sea. it also granted him brittany, "for his livelihood". at the time, brittany was an independent land which france had not been able to conquer. in exchange, rollo promised the king his loyalty and military assistance when needed. also rollo also agreed to be baptised and to marry gisela, the king's daughter. the territory given rollo is about the same as upper normandy. this would grow to become normandy under rollo's descendants. - wikepedia