Solve sqrt{1^x+9+16}=lambdasqrt{x^2+(y-5)^2+(2-1)^2}

$$\sqrt { 1 ^ { x } + 9 + 16 } = \lambda \sqrt { x ^ { 2 } + ( y - 5 ) ^ { 2 } + ( 2 - 1 ) ^ { 2 } }$$

Solve for x (complex solution)

$$x=-\sqrt{-y^{2}+10y-26+\frac{26}{\lambda ^{2}}}$$

$$x=\sqrt{-y^{2}+10y-26+\frac{26}{\lambda ^{2}}}\text{, }arg(\sqrt{\frac{1}{\lambda ^{2}}}\lambda )<\pi \text{ and }\lambda \neq 0$$

Solve for y (complex solution)

$$y=-\sqrt{-x^{2}-1+\frac{26}{\lambda ^{2}}}+5$$

$$y=\sqrt{-x^{2}-1+\frac{26}{\lambda ^{2}}}+5\text{, }\lambda \neq 0\text{ and }arg(\sqrt{\frac{1}{\lambda ^{2}}}\lambda )<\pi$$

Solve for x

$$x=\frac{\sqrt{10y\lambda ^{2}-\left(y\lambda \right)^{2}-26\lambda ^{2}+26}}{\lambda }$$

$$x=-\frac{\sqrt{10y\lambda ^{2}-\left(y\lambda \right)^{2}-26\lambda ^{2}+26}}{\lambda }\text{, }\lambda >0\text{ and }\lambda \leq \sqrt{-\frac{26}{-y^{2}+10y-26}}$$

Solve for y

$$y=\frac{\sqrt{26-\lambda ^{2}-\left(x\lambda \right)^{2}}}{\lambda }+5$$

$$y=-\frac{\sqrt{26-\lambda ^{2}-\left(x\lambda \right)^{2}}}{\lambda }+5\text{, }\lambda \leq \sqrt{26}\text{ and }|x|\leq \frac{\sqrt{26-\lambda ^{2}}}{\lambda }\text{ and }\lambda >0$$