Solve 6/x^2+25/y^2=1

$$\frac { 6 } { x ^ { 2 } } + \frac { 25 } { y ^ { 2 } } = 1$$

Solve for x (complex solution)

$$x=-\sqrt{6}i\left(25-y^{2}\right)^{-\frac{1}{2}}y$$

$$x=\sqrt{6}i\left(25-y^{2}\right)^{-\frac{1}{2}}y\text{, }y\neq 0\text{ and }y\neq 5\text{ and }y\neq -5$$

Solve for y (complex solution)

$$y=-5i\left(6-x^{2}\right)^{-\frac{1}{2}}x$$

$$y=5i\left(6-x^{2}\right)^{-\frac{1}{2}}x\text{, }x\neq 0\text{ and }x\neq -\sqrt{6}\text{ and }x\neq \sqrt{6}$$

Solve for x

$$x=\sqrt{-\frac{6}{25-y^{2}}}y$$

$$x=-\sqrt{-\frac{6}{25-y^{2}}}y\text{, }|y|>5\text{ and }y\neq 0$$

Solve for y

$$y=5\sqrt{-\frac{1}{6-x^{2}}}x$$

$$y=-5\sqrt{-\frac{1}{6-x^{2}}}x\text{, }|x|>\sqrt{6}\text{ and }x\neq 0$$