imsuck's vault

minimum sum of distances to asymptotes

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Case deg(1)deg(1)

𝑦=3π‘₯+8π‘₯+2 𝑆=|π‘₯+2|+|π‘¦βˆ’3|=|π‘₯+2|+2|π‘₯+2|

𝑆 is minimized when |π‘₯+2|=√2 via AM-GM inequality (min𝑆=2√2), a classic case of sum of linear and reciprocal.

Case deg(2)deg(1)

Too hard will fill in later but the idea is pretty similarβ€”reducing to AM-GM.

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