The ellipse, parabola, and hyperbola have the following normal forms:

• • ellipse (and circle): $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ where 0 < b ≤ a.

• • parabola: y² =  4ax where 0 < a.

• • hyperbola: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ where 0 < a,b.

By means of a rotation and translation, any non-degenerate conic can be transformed into one of the above forms, and no two distinct normal forms are congruent. See also quadrics.