Create custom projection using either QGIS (or ArcGIS Desktop)?

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I have searched for an answer to this but don't see anything relating to what I am trying to do.

What I have are a series of Geographic Coordinates, Latitude, Longitude, Ellipsoid heights.

What I want are a local system which is translated from NAD83/UTM.

I know the parameters of the shift which works with UTM Zone 9N.

My parameters are:

Origin North: 5984910.533m,Origin East: 519681.595m

Trans North: 4973.397m,Trans East: 2068.553m

Rotation: 10°12’53”,Scale: 1.0003933608


<strong><b>Trans Height:

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