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Explanation: I think most French speakers would just use "prive". Sometimes people use a specialised word which sounds similar to the word they should use (e.g.English speakers saying "usage" when they just mean "use").
"Privatif" is a term meaning "privative", which the Oxford Dictionary defines as "denoting the privation or absence of a quality etc."
Harrap's Standard French and English Dictionary, Part 1 The Australian Concise English Dictionary
Robin Salmon Australia Local time: 20:03 Native speaker of: English PRO pts in pair: 164
Explanation: "privatif" meaning private, is used when comparing different parts of co-owned property.
I am a home-owner and whilst the house stands in a garden which we own along with the bricks and mortar, beyond a certain limit, the land around is co-owned. It is a "co-propriété" with each owner having a "partie privative" and a share in the "parties communes".