Solve xy-sqrt{4-x^2}=0

$$x y - \sqrt { 4 - x ^ { 2 } } = 0$$

Solve for y (complex solution)

$$y=\frac{\sqrt{4-x^{2}}}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add \sqrt{4-x^{2}} to both sides. Anything plus zero gives itself.

$$xy=\sqrt{4-x^{2}}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{\sqrt{4-x^{2}}}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{\sqrt{4-x^{2}}}{x}$$

Solve for y

$$y=\frac{\sqrt{4-x^{2}}}{x}$$

$$x\neq 0\text{ and }|x|\leq 2$$

Steps for Solving Linear Equation

Add \sqrt{4-x^{2}} to both sides. Anything plus zero gives itself.

$$xy=\sqrt{4-x^{2}}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{\sqrt{4-x^{2}}}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{\sqrt{4-x^{2}}}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=2i\left(-y^{2}-1\right)^{-\frac{1}{2}}\text{, }&y\neq i\text{ and }y\neq -i\text{ and }\left(y=0\text{ or }arg(2i\left(-y^{2}-1\right)^{-\frac{1}{2}}y)<\pi \right)\\x=-2i\left(-y^{2}-1\right)^{-\frac{1}{2}}\text{, }&y\neq i\text{ and }y\neq -i\text{ and }\left(y=0\text{ or }arg(-2i\left(-y^{2}-1\right)^{-\frac{1}{2}}y)<\pi \right)\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{2}{\sqrt{y^{2}+1}}\text{, }&y\leq 0\\x=\frac{2}{\sqrt{y^{2}+1}}\text{, }&y\geq 0\end{matrix}\right.$$