Parametric Equation/Examples/Ellipse

Examples of Parametric Equations

Let $\EE$ be the ellipse embedded in a Cartesian plane with the equation:

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

This can be expressed in parametric equations as:

\(\ds x\)

\(=\)

\(\ds a \cos \phi\)

\(\ds y\)

\(=\)

\(\ds b \sin \phi\)

where $\phi$ is the parameter representing the eccentric angle of the point $\paren {x, y}$ on $\EE$.

Each point on $\CC$ corresponds exactly to a value of $\phi$ such that $\phi \in \hointr 0 {2 \pi}$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): parametric equations
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): parametric equations