Semi-major and Semi-minor Axis of an Ellipse

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Semi-major and Semi-minor Axis of an Ellipseellipse 1ellipse 2

The 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

\(a = \frac{A}{\pi b} \)          \( axis \; a \;=\;  \frac{ area }{ Pi \;\;x\;\; axis \; b} \)

\(a = \frac {l} {1- \epsilon^2} \)          \( axis \; a \;=\;  \frac { semi-latus \; rectum } { 1 \;-\; eccentricity^2} \)

\(b = \frac{A}{\pi a} \)          \( axis \; b \;=\; \frac{ area }{ Pi  \;\;x\;\; axis \; a} \)

\(b = a \sqrt {1- \epsilon^2} \)          \( axis \; b \;=\; semi-major \; axis \; \sqrt { \; 1 \;-\; eccentricity^2} \)

Where:

\(a\) = length semi-major axis

\(b\) = length semi-minor axis

\(A\) = area

\(\pi\) = Pi

\(l\) = semi-latus rectum

\(\epsilon\) (Greek symbol epsilon) = eccentricity