The ellipse parallel curves for (outward) offset 
of an ellipse with semi-axis lengths 
and 
are given by
 |  |  |
(1)
|
 |  |  |
(2)
|
The plots above show ellipse parallel curves for ellipses with 
and 0.9.
Each parallel curve can be written as an octic algebraic curve in 
and 
.
For 
and outward offset 
, let
 |
(3)
|
where 
is the perimeter of the ellipse and 
is the complete
elliptic integral of the second kind. The perimeter
and enclosed area of the parallel
curve are then
 |
(4)
|
and
 |
(5)
|
respectively. These formulas apply to outward offsets. Inward offsets require separate treatment after cusps or self-intersections appear.
The plot above shows a close-up for "inward" ellipse parallel curves. Talbot's curve resembles these curves.
