Equation of Ellipse in Reduced Form

Theorem

Let $K$ be an ellipse aligned in a cartesian coordinate plane in reduced form.

Let:

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

Cartesian Frame

The equation of $K$ is:

$\dfrac {x^2} {a^2} + \dfrac {y^2} {b^2} = 1$

Parametric Form

The equation of $K$ in parametric form is:

$x = a \cos \theta, y = b \sin \theta$