Answer
A circle will have its equation in the form $x^2+y^2=z^2$ where $z$ is any nonzero or imaginary number. A parabola will have its equation in the form $y=x^2$ or $x=y^2$.
Work Step by Step
An ellipse will have its equation in the form $(x^2/a^2) + (y^2/b^2) = 1$, where $a \ne 0$ and $b \ne 0$. A hyperbola would have its equation in the form $(x^2/a^2) - (y^2/b^2) = 1$ or $(y^2/b^2) - (x^2/a^2) = 1$, where $a \ne 0$ and $b \ne 0$.
