Solve x^2+y^2=cy

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

Solve for c (complex solution)

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Divide x^{2}+y^{2} by y.

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

Solve for c

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Divide x^{2}+y^{2} by y.

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

Solve for x (complex solution)

$$x=-i\sqrt{y}\sqrt{y-c}$$

$$x=i\sqrt{y}\sqrt{y-c}$$

Solve for x

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

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