Equation of Ellipse in Reduced Form

Theorem
Let $K$ be an ellipse aligned in a cartesian coordinate plane such that:


 * The major axis of $K$ is aligned with the $x$-axis
 * The minor axis of $K$ is aligned with the $y$-axis.

Let:


 * The major axis of $K$ have length $2 a$
 * The minor axis of $K$ have length $2 b$.