Solve y=sqrt{-x^2+b}

$$y = \sqrt { - x ^ { 2 } + b }$$

Solve for b

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

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{-x^{2}+b}=y$$

Square both sides of the equation.

$$b-x^{2}=y^{2}$$

Subtract -x^{2} from both sides of the equation.

$$b-x^{2}-\left(-x^{2}\right)=y^{2}-\left(-x^{2}\right)$$

Subtracting -x^{2} from itself leaves 0.

$$b=y^{2}-\left(-x^{2}\right)$$

Subtract -x^{2} from y^{2}.

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

Solve for b (complex solution)

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

$$arg(y)<\pi \text{ or }y=0$$

Solve for x (complex solution)

$$x=-\sqrt{b-y^{2}}$$

$$x=\sqrt{b-y^{2}}\text{, }arg(y)<\pi \text{ or }y=0$$

Solve for x

$$x=\sqrt{b-y^{2}}$$

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