Solve x^2+4y^2=4ay

$$x ^ { 2 } + 4 y ^ { 2 } = 4 a y$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{x^{2}}{4y}+y\text{, }&y\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$4ay=x^{2}+4y^{2}$$

The equation is in standard form.

$$4ya=x^{2}+4y^{2}$$

Divide both sides by 4y.

$$\frac{4ya}{4y}=\frac{x^{2}+4y^{2}}{4y}$$

Dividing by 4y undoes the multiplication by 4y.

$$a=\frac{x^{2}+4y^{2}}{4y}$$

Divide x^{2}+4y^{2} by 4y.

$$a=\frac{x^{2}}{4y}+y$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x^{2}}{4y}+y\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$4ay=x^{2}+4y^{2}$$

The equation is in standard form.

$$4ya=x^{2}+4y^{2}$$

Divide both sides by 4y.

$$\frac{4ya}{4y}=\frac{x^{2}+4y^{2}}{4y}$$

Dividing by 4y undoes the multiplication by 4y.

$$a=\frac{x^{2}+4y^{2}}{4y}$$

Divide x^{2}+4y^{2} by 4y.

$$a=\frac{x^{2}}{4y}+y$$

Solve for x (complex solution)

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

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

Solve for x

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

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