digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

The semi-major (in red*) and semi-minor axis (in blue*) of an ellipse.
(* on some browsers)

In geometry, the semi-minor axis (also semiminor axis) is a line segment associated with most conic sections (that is, with ellipses and hyperbolas) that is at right angles with the semi-major axis and has one end at the center of the conic section. It is one of the axes of symmetry for the curve: in an ellipse, the shorter one; in a hyperbola, the one that does not intersect the hyperbola.

## Ellipse

The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the foci) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge.

The semi-minor axis b is related to the semi-major axis $a$ through the eccentricity $e$ and the semi-latus rectum $l$, as follows:

$b = a \sqrt{1-e^2}\,\!$
$al=b^2\,\!$.

The semi-minor axis of an ellipse is the geometric mean of the maximum and minimum distances $r_{max}$ and $r_{min}$ of the ellipse from a focus — that is, of the distances from a focus to the endpoints of the major axis:

$b = \sqrt{r_{max}r_{min}}.$

A parabola can be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction, keeping l fixed. Thus a and b tend to infinity, a faster than b.

The length of the semi-minor axis could also be found using the following formula[1],

$2b = \sqrt{(p+q^2)-f^2}$ where f is the distance between the foci, p and q are the distances from each focus to any point in the ellipse.

## Hyperbola

In a hyperbola, a conjugate axis or minor axis of length 2b, corresponding to the minor axis of an ellipse, can be drawn perpendicular to the transverse axis or major axis, the latter connecting the two vertices (turning points) of the hyperbola, with the two axes intersecting at the center of the hyperbola. The endpoints (0, ±b) of the minor axis lie at the height of the asymptotes over/under the hyperbola's vertices. Either half of the minor axis is called the semi-minor axis, of length b. Denoting the semi-major axis length (distance from the center to a vertex) as a, the semi-minor and semi-major axes' lengths appear in the equation of the hyperbola relative to these axes as follows:

$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1.$

The semi-minor axis and the semi-major axis are related through the eccentricity, as follows:

$b = a \sqrt{e^2-1}.$

Note that in a hyperbola b can be larger than a. [1]

## References

1. ^ http://www.mathopenref.com/ellipseaxes.html,"Major / Minor axis of an ellipse",Math Open Reference, 12 May 2013
 94 videos foundNext >
 Ellipse1of8 Constructing on ellipse from its definition.This is the first video in a series of eight that takes a comprehensive look at ellipses. In this video we start with the definition of an ellipse: the set o... Hindi : Relation between major axis, minor axis and distance of the focus.. - Ch 11 - CBSE 11th MathIn this video we will learn relationship between semi-major axis, semi-minor axis and the distance of the focus from the centre of the ellipse. Subscribe to ... An orbit which could almost have worked, almost!This video talks about the hohmann transfer which allows the LM to go from the CM's orbit to the lower 50000 feet orbit from which the landing procedure sta... Conic section for JEE Solution of AIEEE 2012 Maths problem based on ellipseA conceptual problem from Conic section ; An ellipse is drawn by taking a diameter of the given circle as its semi minor axis and a diameter of anothe circle... The Earth. Exploration of....Exploration of the planet Earth. Discovery of rock, sand, 78% nitrogen and 21% oxygen atmosphere, Water and carbon-based life forms. Details: Epoch J2000 Aph... Points around an Ellipsehttp://demonstrations.wolfram.com/PointsAroundAnEllipse/ The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new e... Hannah Montana Math Videoextra credit Lyrics: I've got a tangent function I'm gonna calculate I know the law of cosines What am ambiguous case. I know the unit circle In radians and ... Tutorial - Portable Six-axis Frame Quarry - Construction [Part 1 of 3]Utilising TeamPantsMadness's EG-Drive Mk6 ( http://youtu.be/zU724YG3mbM ) with a few minor adjustments, this RedPower2 Frame-based Quarry can mine out a larg... Tutorial - Portable Six-axis Frame Quarry - Basic Programming [Part 2 of 3]Utilising TeamPantsMadness's EG-Drive Mk6 ( http://youtu.be/zU724YG3mbM ) with a few minor adjustments, this RedPower2 Frame-based Quarry can mine out a larg... Using the AD2 Hinge Axis Recorder
 94 videos foundNext >

We're sorry, but there's no news about "Semi-minor axis" right now.

 Limit to books that you can completely read online Include partial books (book previews) .gsc-branding { display:block; }

Oops, we seem to be having trouble contacting Twitter