Finding the equation of a circle and hyperbola

Question

The two graphs above are the graphs of functions $y=\sqrt{1-x^2}$ and $y=\sqrt{1+x^2}$.

How do you figure out the equations of the corresponding circle and hyperbola?

Answer 1

Squaring either equation gives you what you want: $y^2=1-x^2$ for the circle, and $y^2=1+x^2$ for the hyperbola. Rearrange either any way you want.