Solve fx^2+y^2=100

$$f x ^ { 2 } + y ^ { 2 } = 100$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{y^{2}-100}{x^{2}}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&\left(y=-10\text{ or }y=10\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

$$fx^{2}=100-y^{2}$$

The equation is in standard form.

$$x^{2}f=100-y^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}f}{x^{2}}=\frac{100-y^{2}}{x^{2}}$$

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

$$f=\frac{100-y^{2}}{x^{2}}$$

Divide 100-y^{2} by x^{2}.

$$f=\frac{\left(10-y\right)\left(y+10\right)}{x^{2}}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{y^{2}-100}{x^{2}}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ and }|y|=10\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

$$fx^{2}=100-y^{2}$$

The equation is in standard form.

$$x^{2}f=100-y^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}f}{x^{2}}=\frac{100-y^{2}}{x^{2}}$$

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

$$f=\frac{100-y^{2}}{x^{2}}$$

Divide 100-y^{2} by x^{2}.

$$f=\frac{\left(10-y\right)\left(y+10\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-if^{-\frac{1}{2}}\sqrt{y^{2}-100}\text{; }x=if^{-\frac{1}{2}}\sqrt{y^{2}-100}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&\left(y=-10\text{ or }y=10\right)\text{ and }f=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{-\frac{y^{2}-100}{f}}\text{; }x=-\sqrt{-\frac{y^{2}-100}{f}}\text{, }&\left(|y|\geq 10\text{ and }f<0\right)\text{ or }\left(f>0\text{ and }|y|\leq 10\right)\\x\in \mathrm{R}\text{, }&f=0\text{ and }|y|=10\end{matrix}\right.$$