Polar equation of ellipse

An ellipse is a rotation and/or translation of a plane figure whose equation in polar coordinates is

where the origin is at one focus of the ellipse, a is the length of the semimajor axis, b is the length of the semiminor axis, and c is the distance from the focus to the center of the ellipse.

Alternatively, an ellipse is a rotation and/or translation of the figure with polar equation

where the origin is at one focus of the ellipse, e is the eccentricity (between 0 and 1), and the directrix is d units from the focus.