Solve [(x^2+y^2)-(w-y)^2+2y(xquady)]div4y=1

$$[ ( x ^ { 2 } + y ^ { 2 } ) - ( w - y ) ^ { 2 } + 2 y ( x \quad y ) ] \div 4 y = 1$$

Solve for w (complex solution)

$$w=-\frac{\sqrt{2xy^{4}+y^{4}-4y+\left(xy\right)^{2}}}{y}+y$$

$$w=\frac{\sqrt{2xy^{4}+y^{4}-4y+\left(xy\right)^{2}}}{y}+y\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y\left(y^{5}-2wy^{2}+yw^{2}+4\right)}-y^{3}}{y}$$

$$x=-\frac{\sqrt{y\left(y^{5}-2wy^{2}+yw^{2}+4\right)}+y^{3}}{y}\text{, }y\neq 0$$

Solve for w

$$w=-\frac{\sqrt{2xy^{4}+y^{4}-4y+\left(xy\right)^{2}}}{y}+y$$

$$w=\frac{\sqrt{2xy^{4}+y^{4}-4y+\left(xy\right)^{2}}}{y}+y\text{, }\left(4y^{6}-4y^{4}+16y\leq 0\text{ or }y^{6}-y^{4}+4y<0\text{ or }y<0\text{ or }x\leq -\frac{\sqrt{y^{6}-y^{4}+4y}}{y}-y^{2}\text{ or }x\geq \frac{\sqrt{y^{6}-y^{4}+4y}}{y}-y^{2}\right)\text{ and }\left(4y^{6}-4y^{4}+16y\leq 0\text{ or }y^{6}-y^{4}+4y<0\text{ or }y>0\text{ or }x\geq -\frac{\sqrt{y^{6}-y^{4}+4y}}{y}-y^{2}\text{ or }x\leq \frac{\sqrt{y^{6}-y^{4}+4y}}{y}-y^{2}\right)\text{ and }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{y\left(y^{5}-2wy^{2}+yw^{2}+4\right)}-y^{3}}{y}$$

$$x=-\frac{\sqrt{y\left(y^{5}-2wy^{2}+yw^{2}+4\right)}+y^{3}}{y}\text{, }\left(y^{5}-2wy^{2}+yw^{2}\geq -4\text{ and }y>0\right)\text{ or }\left(y^{5}-2wy^{2}+yw^{2}\leq -4\text{ and }y<0\right)$$