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Question Number 190532 by MathsFan last updated on 05/Apr/23

$${10\mathrm{x}}^2-9\mathrm{xy}+{2\mathrm{y}}^2=10$$$$\mathrm{please}\mathrm{how}\mathrm{do}\mathrm{I}\mathrm{find}\mathrm{the}\mathrm{ratio}\mathrm{of}$$$$\mathrm{x}:\mathrm{y}$$

Answered by Frix last updated on 05/Apr/23

$${\mathrm{There}}^{\prime }\mathrm{s}\mathrm{no}\mathrm{general}\mathrm{ratio}.$$$$10x^2-9xy+2y^2=10\iff y=\frac{9x\pm \sqrt{x^2+80}}{4}$$$$\mathrm{This}\mathrm{is}\mathrm{a}\mathrm{hyperbola}.\mathrm{The}\mathrm{slopes}\mathrm{of}\mathrm{its}\mathrm{axes}$$$$\mathrm{are}-\frac{4}{9}\mathrm{and}\frac{9}{4}.$$

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