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Question Number 64097 by ajfour last updated on 13/Jul/19

Commented by ajfour last updated on 13/Jul/19

$$Findsidelength\mathit{s}ofequalsided$$$$hexagoninscribedinellipseof$$$$parameters\mathit{a}and\mathit{b}.$$

Answered by ajfour last updated on 13/Jul/19

$$a\cos \theta =\frac{s}{2}$$$$s^2={(a-\frac{s}{2})}^2+b^2(1-\frac{s^2}{4a^2})$$$$s^2(\frac{3}{4}+\frac{b^2}{4a^2})+as-a^2-b^2=0$$$$s=\frac{-a+\sqrt{a^2+(a^2+b^2)(3+\frac{b^2}{a^2})}}{\frac{1}{2}(3+\frac{b^2}{a^2})}.$$$$Ifa=b=r$$$$s=r.$$

Commented by mr W last updated on 13/Jul/19

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