Solve byx^2+y^2=4

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

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{y^{2}-4}{yx^{2}}\text{, }&x\neq 0\text{ and }y\neq 0\\b\in \mathrm{C}\text{, }&\left(y=-2\text{ or }y=2\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

$$byx^{2}=4-y^{2}$$

The equation is in standard form.

$$yx^{2}b=4-y^{2}$$

Divide both sides by yx^{2}.

$$\frac{yx^{2}b}{yx^{2}}=\frac{4-y^{2}}{yx^{2}}$$

Dividing by yx^{2} undoes the multiplication by yx^{2}.

$$b=\frac{4-y^{2}}{yx^{2}}$$

Divide -y^{2}+4 by yx^{2}.

$$b=\frac{\left(2-y\right)\left(y+2\right)}{yx^{2}}$$

Solve for b

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

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

$$byx^{2}=4-y^{2}$$

The equation is in standard form.

$$yx^{2}b=4-y^{2}$$

Divide both sides by yx^{2}.

$$\frac{yx^{2}b}{yx^{2}}=\frac{4-y^{2}}{yx^{2}}$$

Dividing by yx^{2} undoes the multiplication by yx^{2}.

$$b=\frac{4-y^{2}}{yx^{2}}$$

Divide -y^{2}+4 by yx^{2}.

$$b=\frac{\left(2-y\right)\left(y+2\right)}{yx^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-ib^{-\frac{1}{2}}y^{-\frac{1}{2}}\sqrt{y^{2}-4}\text{; }x=ib^{-\frac{1}{2}}y^{-\frac{1}{2}}\sqrt{y^{2}-4}\text{, }&y\neq 0\text{ and }b\neq 0\\x\in \mathrm{C}\text{, }&\left(y=-2\text{ or }y=2\right)\text{ and }b=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{-\frac{y^{2}-4}{by}}\text{; }x=-\sqrt{-\frac{y^{2}-4}{by}}\text{, }&\left(y\geq -2\text{ and }y<0\text{ and }b<0\right)\text{ or }\left(y\leq 2\text{ and }b>0\text{ and }y>0\right)\text{ or }\left(y\geq 2\text{ and }b<0\right)\text{ or }\left(b>0\text{ and }y\leq -2\right)\\x\in \mathrm{R}\text{, }&b=0\text{ and }|y|=2\end{matrix}\right.$$