Semi-major and Semi-minor Axis of an Ellipse

Written by Jerry Ratzlaff on . Posted in Plane Geometry

ellipse 1ellipse 2The major axis is always the longest axis in an ellipse.

The minor axis is always the shortest axis in an ellipse.

Semi-major and Semi-minor Axis of an Ellipse formula

\(\large{ a = \frac{A}{\pi \;b} }\)

\(\large{ a = \frac {l} {1- \epsilon^2} }\)

\(\large{ b = \frac{A}{\pi \;a} }\)

\(\large{ b = a \sqrt {1- \epsilon^2} }\)

Where:

\(\large{ a }\) = length semi-major axis

\(\large{ b }\) = length semi-minor axis

\(\large{ A }\) = area

\(\large{ \pi }\) = Pi

\(\large{ l }\) = semi-latus rectum

\(\large{ \epsilon }\)  (Greek symbol epsilon) = eccentricity