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here is a simpler [solution] that someone else came up with.
https://www.usna.edu/Users/physics/mungan/_files/documents/Scholarship/DescentRampTrack.pdf
3x^2 - 2yx + (4 - y^2) = 0 (4)
x = (y ± 2*sqrt(y^2 - 3)) / 3 (5)
But as Y decreases in value, these two values of X converge toward
one common value that must evidently give the minimum
3x^2 - 2x√y + (4 - y^2) = 0 (4')