Solve 1=left(x-1right)^2/4+left(y-2right)^2/9

$$1 = \frac{ { \left(x-1 \right) }^{ 2 } }{ 4 } + \frac{ { \left(y-2 \right) }^{ 2 } }{ 9 }$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{5-y}\sqrt{y+1}}{3}+1$$

$$x=\frac{2\sqrt{5-y}\sqrt{y+1}}{3}+1$$

Solve for y (complex solution)

$$y=-\frac{3\sqrt{3-x}\sqrt{x+1}}{2}+2$$

$$y=\frac{3\sqrt{3-x}\sqrt{x+1}}{2}+2$$

Solve for x

$$x=\frac{-2\sqrt{\left(5-y\right)\left(y+1\right)}+3}{3}$$

$$x=\frac{2\sqrt{\left(5-y\right)\left(y+1\right)}+3}{3}\text{, }y\geq -1\text{ and }y\leq 5$$

Solve for y

$$y=\frac{-3\sqrt{\left(3-x\right)\left(x+1\right)}+4}{2}$$

$$y=\frac{3\sqrt{\left(3-x\right)\left(x+1\right)}+4}{2}\text{, }x\geq -1\text{ and }x\leq 3$$