Solve y^2=(1-x^2)^9

$$y ^ { 2 } = ( 1 - x ^ { 2 } ) ^ { 9 }$$

Solve for x (complex solution)

$$x\in \sqrt{e^{\frac{7\pi i}{9}}y^{\frac{2}{9}}+1},-\sqrt{e^{\frac{7\pi i}{9}}y^{\frac{2}{9}}+1},-\sqrt{e^{\frac{5\pi i}{9}}y^{\frac{2}{9}}+1},\sqrt{e^{\frac{5\pi i}{9}}y^{\frac{2}{9}}+1},-\sqrt{e^{\frac{\pi i}{3}}y^{\frac{2}{9}}+1},\sqrt{e^{\frac{\pi i}{3}}y^{\frac{2}{9}}+1},-\sqrt{e^{\frac{\pi i}{9}}y^{\frac{2}{9}}+1},\sqrt{e^{\frac{\pi i}{9}}y^{\frac{2}{9}}+1},-\sqrt{e^{\frac{17\pi i}{9}}y^{\frac{2}{9}}+1},\sqrt{e^{\frac{17\pi i}{9}}y^{\frac{2}{9}}+1},-\sqrt{e^{\frac{5\pi i}{3}}y^{\frac{2}{9}}+1},\sqrt{e^{\frac{5\pi i}{3}}y^{\frac{2}{9}}+1},-\sqrt{e^{\frac{13\pi i}{9}}y^{\frac{2}{9}}+1},\sqrt{e^{\frac{13\pi i}{9}}y^{\frac{2}{9}}+1},-\sqrt{1-y^{\frac{2}{9}}},\sqrt{1-y^{\frac{2}{9}}},-\sqrt{e^{\frac{11\pi i}{9}}y^{\frac{2}{9}}+1},\sqrt{e^{\frac{11\pi i}{9}}y^{\frac{2}{9}}+1}$$

Solve for y (complex solution)

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

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

Solve for x

$$x=\sqrt{1-y^{\frac{2}{9}}}$$

$$x=-\sqrt{1-y^{\frac{2}{9}}}\text{, }|y|\leq 1$$

Solve for y

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

$$y=-\left(1-x^{2}\right)^{\frac{9}{2}}\text{, }|x|\leq 1$$