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Question Number 49737 by ajfour last updated on 09/Dec/18

Commented by ajfour last updated on 09/Dec/18

$$Findparameters\mathit{a}and\mathit{b}of$$$$ellipsecircumscribingarectangle$$$$ofsides\mathit{l}and\mathit{h}.$$

Answered by ajfour last updated on 09/Dec/18

$$\frac{l^2}{a^2}+\frac{h^2}{b^2}=4,letT=a^2{b}^2$$$$T=a^2\left(\frac{h^2}{4-\frac{l^2}{a^2}}\right)=\frac{a^4{h}^2}{4a^2-l^2}$$$$\frac{dT}{da}=\frac{4h^2{a}^3(4a^2-l^2)-8a^5{h}^2}{{(4a^2-l^2)}^2}$$$$\frac{dT}{da}=0\Rightarrow a=\frac{l}{\sqrt{2}},b=\frac{h}{\sqrt{2}}.$$

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