Ratkaise x^2+y^2-4a^2=2x+2ay

$$x ^ { 2 } + y ^ { 2 } - 4 a ^ { 2 } = 2 x + 2 a y$$

Ratkaise muuttujan a suhteen (complex solution)

$$a=\frac{-\sqrt{4x^{2}-8x+5y^{2}}-y}{4}$$

$$a=\frac{\sqrt{4x^{2}-8x+5y^{2}}-y}{4}$$

Ratkaise muuttujan x suhteen (complex solution)

$$x=\sqrt{1+4a^{2}+2ay-y^{2}}+1$$

$$x=-\sqrt{1+4a^{2}+2ay-y^{2}}+1$$

Ratkaise muuttujan a suhteen

$$a=\frac{-\sqrt{4x^{2}-8x+5y^{2}}-y}{4}$$

$$a=\frac{\sqrt{4x^{2}-8x+5y^{2}}-y}{4}\text{, }x\leq -\frac{\sqrt{4-5y^{2}}}{2}+1\text{ or }x\geq \frac{\sqrt{4-5y^{2}}}{2}+1\text{ or }|y|\geq \frac{2\sqrt{5}}{5}$$

Ratkaise muuttujan x suhteen

$$x=\sqrt{1+4a^{2}+2ay-y^{2}}+1$$

$$x=-\sqrt{1+4a^{2}+2ay-y^{2}}+1\text{, }y\geq -\sqrt{5a^{2}+1}+a\text{ and }y\leq \sqrt{5a^{2}+1}+a$$