Equation of Ellipse in Reduced Form
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Theorem
Let $K$ be an ellipse aligned in a cartesian 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:
\(\ds x\) | \(=\) | \(\ds a \cos \theta\) | ||||||||||||
\(\ds y\) | \(=\) | \(\ds b \sin \theta\) |
where $\theta$ is the eccentric angle of the point $P = \tuple {x, y}$ with respect to $K$.