Equation of Ellipse in Reduced Form

From ProofWiki
Jump to navigation Jump to search


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


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:

\(\ds x\) \(=\) \(\ds a \cos \theta\)
\(\ds y\) \(=\) \(\ds b \sin \theta\)

where $\theta$ is the eccentric angle of the point $P = \tuple {x, y}$ with respect to $K$.

Also see