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Question Number 155400 by TVTA last updated on 30/Sep/21

$$x^2+x+5xy+6y^2+2y-2=0$$

Commented by MJS_new last updated on 30/Sep/21

$$\mathrm{hyperbola}\mathrm{with}\mathrm{center}\left[\begin{array}{c}2\\ -1\end{array}\right]\mathrm{and}\mathrm{axes}$$$$a=2\sqrt{-7+5\sqrt{2}}$$$$b=2\sqrt{7+5\sqrt{2}}$$$$\mathrm{rotated}\mathrm{by}\frac{3\pi }{8}=67.5°$$$$\mathrm{the}\mathrm{transformed}\mathrm{equation}\mathrm{is}$$$$\frac{x^2}{-28+20\sqrt{2}}-\frac{y^2}{28+20\sqrt{2}}=1$$

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