\left\{ \begin{array} { l } { \frac { x } { y } - \frac { y } { x } = \frac { 1 } { 4 } } \\ { x ^ { 2 } + y ^ { 2 } = 612 } \end{array} \right.
Solve for x, y (complex solution)
x=-\frac{3\left(\sqrt{2210}+65\sqrt{34}\right)\sqrt{65-\sqrt{65}}}{520}\approx -18.546013825\text{, }y=-\frac{3\sqrt{2210\left(65-\sqrt{65}\right)}}{65}\approx -16.372091229
x=\frac{3\left(\sqrt{2210}-65\sqrt{34}\right)\sqrt{\sqrt{65}+65}}{520}\approx -16.372091229\text{, }y=\frac{3\sqrt{2210\left(\sqrt{65}+65\right)}}{65}\approx 18.546013825
x=\frac{24\sqrt{2210}\sqrt{\sqrt{65}+65}}{520}\approx 18.546013825\text{, }y=\frac{3\sqrt{2210\left(65-\sqrt{65}\right)}}{65}\approx 16.372091229
x=\frac{24\sqrt{2210}\sqrt{65-\sqrt{65}}}{520}\approx 16.372091229\text{, }y=-\frac{3\sqrt{2210\left(\sqrt{65}+65\right)}}{65}\approx -18.546013825
Solve for x, y
x=\frac{3\sqrt{143650-2210\sqrt{65}}}{65}\approx 16.372091229\text{, }y=-\frac{3\sqrt{2210\sqrt{65}+143650}}{65}\approx -18.546013825
x=-\frac{3\sqrt{143650-2210\sqrt{65}}}{65}\approx -16.372091229\text{, }y=\frac{3\sqrt{2210\sqrt{65}+143650}}{65}\approx 18.546013825
x=-\frac{3\sqrt{2210\sqrt{65}+143650}}{65}\approx -18.546013825\text{, }y=-\frac{3\sqrt{143650-2210\sqrt{65}}}{65}\approx -16.372091229
x=\frac{3\sqrt{2210\sqrt{65}+143650}}{65}\approx 18.546013825\text{, }y=\frac{3\sqrt{143650-2210\sqrt{65}}}{65}\approx 16.372091229
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