Segment of an Ellipse

on . Posted in Plane Geometry

  • ellipse segment 3hollow ellipse s major s minor 3Ellipse segment (a two-dimensional figure) is an interior part of an ellipse bound by a chord and an ellipse.
  • Chord is a line segment on the interior of the ellipse.
  • Major axis is always the longest axis in an ellipse.
  • Minor axis is always the shortest axis in an ellipse.
  • Semi-major axis is half of the longest axis of an ellipse.
  • Semi-minor axis is half of the shortest axis of an ellipse.

 

 

 

 

Segment Area formula

\(\large{ A_{area} \;=\; \frac{c\;d}{4} \;  \left[ arccos \left( 1-\frac{2\;h}{c} \right) - \left( 1-\frac{2\;h}{c} \right) \; \sqrt{ \frac{4\;h}{c} } - \frac{4\;h^2}{c^2}     \right]    }\)
 Symbol English Metric
\( A_{area} \) = area \( in^2 \) \( mm^2 \)
\( h \) = height \( in \) \( mm \)
\( c \) = major axis \( in \) \( mm \)
\( d \) = minor axis \( in \) \( mm \)

 

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Tags: Ellipse