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It does give a result if you consider four different cases for the signs of a and b: f[{g_, h_}, a_, b_] := g[a, 0] && h[b, 0] Minimize[{(e - x)^2 + (n - y)^2, a e + b n == c && #}, {e, n}, Reals] & /@ (f[#, a, b] & /@ Tuples[{Greater, Less}, 2]) The result is too large to ...



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