Solve x^2+y^2=2ay

$$x ^ { 2 } + y ^ { 2 } = 2 a y$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{x^{2}+y^{2}}{2y}\text{, }&y\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2ay=x^{2}+y^{2}$$

The equation is in standard form.

$$2ya=x^{2}+y^{2}$$

Divide both sides by 2y.

$$\frac{2ya}{2y}=\frac{x^{2}+y^{2}}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$a=\frac{x^{2}+y^{2}}{2y}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x^{2}+y^{2}}{2y}\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2ay=x^{2}+y^{2}$$

The equation is in standard form.

$$2ya=x^{2}+y^{2}$$

Divide both sides by 2y.

$$\frac{2ya}{2y}=\frac{x^{2}+y^{2}}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$a=\frac{x^{2}+y^{2}}{2y}$$

Solve for x (complex solution)

$$x=-i\sqrt{y}\sqrt{y-2a}$$

$$x=i\sqrt{y}\sqrt{y-2a}$$

Solve for x

$$x=\sqrt{y\left(2a-y\right)}$$

$$x=-\sqrt{y\left(2a-y\right)}\text{, }\left(y\geq 0\text{ or }y\geq 2a\right)\text{ and }\left(y\leq 0\text{ or }y\leq 2a\right)$$