Equation of Ellipse in Reduced Form/Cartesian Frame/Parametric 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 $2a$
 * The minor axis of $K$ have length $2b$.

The equation of $K$ in parametric form is:
 * $x = a \cos \theta, y = b \sin \theta$

Proof
Let the point $\left({x, y}\right)$ satisfy the equations:
 * $x = a \cos \theta$
 * $y = b \sin \theta$

Then: