semi-minor axis

In geometry, the semi-minor axis (also semiminor axis) applies to ellipses and hyperbolas.

Ellipse

The semi-minor axis of an ellipse is one half of the minor axis, running from the center, halfway between and perpendicular to the line running between the foci, and to the edge of the ellipse. The minor axis is the longest line that runs perpendicular to the major axis. It 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

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.

Hyperbola

The semi-minor axis of a hyperbola is the distance from a top, along the tangent line, to each asymptote; if this is in the y-direction it is b in this equation of the hyperbola:

\frac{\left( x-h \right)^2}{a^2} - \frac{\left( y-k \right)^2}{b^2} = 1

It is related to the semi-major axis through the eccentricity, as follows:

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

Note that in a hyperbola b can be larger than a!

<< Previous

Word Browser

Next >>

soup with risotto
list of massachusetts institute of technology people
walter wyatt
list of picture discs
faisceau
limiting magnitude
iphigeneia at aulis
astronomical catalog
futari wa pretty cure
mike altman
superliner (railcar)

arnines
seal of hawaii
kano (mortal kombat character)
henry putzel, jr.
agenda
imageboard
jason richey
spaghetti strap
henry curtis lind
drogue parachute
eccentric anomaly

melanosome
true anomaly
kintaro (mortal kombat character)
christopher c. kraft, jr.
dairy cattle
mechanism (horology)
woyzeck
mount adams (disambiguation)
train of many colors
texans for truth
collision attack

2004 toronto international film festival
white mountain national forest
francisco l. guzman
41450 medkeff
heardred
rolls royce vulture
neal pollack
woodhaven, queens
cmucl
mridangam
list of yorkshire people