Solve Aquadx^2+y^2=a^2

$$A \quad x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$$

Solve for A (complex solution)

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

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

$$Ax^{2}=a^{2}-y^{2}$$

The equation is in standard form.

$$x^{2}A=a^{2}-y^{2}$$

Divide both sides by x^{2}.

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

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

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

Solve for A

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

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

$$Ax^{2}=a^{2}-y^{2}$$

The equation is in standard form.

$$x^{2}A=a^{2}-y^{2}$$

Divide both sides by x^{2}.

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

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

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

Solve for a (complex solution)

$$a=-\sqrt{Ax^{2}+y^{2}}$$

$$a=\sqrt{Ax^{2}+y^{2}}$$

Solve for a

$$a=\sqrt{Ax^{2}+y^{2}}$$

$$a=-\sqrt{Ax^{2}+y^{2}}\text{, }A\geq -\frac{y^{2}}{x^{2}}\text{ or }x=0$$