# Inner and outer borders of ellipse

I have created an ellipse of constant thickness. What are the shapes for the inner and outer boundaries? I know they are not also ellipses. I was only able to draw the shape in geometry software, and do not know the formulas. Thanks.

• Are you looking for a formula (would parametric do?) or a name? Essentially you extend point $K$ by $\pm r$ perpendicularly to the tangent at $K$ – Henry Jul 19 '18 at 22:32
• If this previous question similar? The accepted answer describes the constructed curve as a parallel curve. – Weather Vane Jul 19 '18 at 22:48
• I would like a formula or formulas, yes. I will be working in POV-Ray, so I'm not sure yet whether a parametric function would be better than an implicit function. – posfan12 Jul 19 '18 at 22:50
• @Weather Vane - Yes that does look like the same question. – posfan12 Jul 19 '18 at 23:00
• How you define the width - along the vertical or through the origin? – Moti Jul 19 '18 at 23:38