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Semi-minor axis

 

 
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Semi-minor axis
 
 
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In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, the semi-minor axis (also semiminor axis) is a line segment
Line segment

In geometry, a line segment is a part of a line that is bounded by two end Point , and contains every point on the line between its end points....
 associated with most conic section
Conic section

File:Conic sections with plane.svgIn mathematics, a conic section is a curve obtained by intersecting a cone with a plane . A conic section is therefore a restriction of a quadric surface to the plane ....
s (that is, with ellipses and hyperbolas). One end of the segment is the center of the conic section, and it is at right angle
Right angle

In geometry and trigonometry, a right angle is an angle of 90 degree s, corresponding to a quarter turn . It can be defined; as the angle such that twice that angle amounts to a half turn, or 180?....
s with the semi-major axis
Semi-major axis

In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
. 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
Ellipse

In mathematics, an ellipse is the apparent shape of a circle viewed obliquely from outside it, as distinct from a hyperbola which is the shape seen from inside....
 is one half of the minor axis, running from the center, halfway between and perpendicular to the line running between the foci
Focus (geometry)

In geometry, the foci, , are a pair of special points used in describing conic sections. The four types of conic sections are the circle, parabola, ellipse, and hyperbola....
, and to the edge of the ellipse.






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Semiminoraxis
In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, the semi-minor axis (also semiminor axis) is a line segment
Line segment

In geometry, a line segment is a part of a line that is bounded by two end Point , and contains every point on the line between its end points....
 associated with most conic section
Conic section

File:Conic sections with plane.svgIn mathematics, a conic section is a curve obtained by intersecting a cone with a plane . A conic section is therefore a restriction of a quadric surface to the plane ....
s (that is, with ellipses and hyperbolas). One end of the segment is the center of the conic section, and it is at right angle
Right angle

In geometry and trigonometry, a right angle is an angle of 90 degree s, corresponding to a quarter turn . It can be defined; as the angle such that twice that angle amounts to a half turn, or 180?....
s with the semi-major axis
Semi-major axis

In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
. 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
Ellipse

In mathematics, an ellipse is the apparent shape of a circle viewed obliquely from outside it, as distinct from a hyperbola which is the shape seen from inside....
 is one half of the minor axis, running from the center, halfway between and perpendicular to the line running between the foci
Focus (geometry)

In geometry, the foci, , are a pair of special points used in describing conic sections. The four types of conic sections are the circle, parabola, ellipse, and hyperbola....
, 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
Semi-major axis

In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
  through the eccentricity
Eccentricity (mathematics)

In mathematics, the eccentricity, denoted e or , is a parameter associated with every Conic section#Eccentricity. It can be thought of as a measure of how much the conic section deviates from being circular....
  and the semi-latus rectum , as follows:

.

A parabola
Parabola

In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface....
 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.

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Hyperbola


The length of the semi-minor axis of a hyperbola
Hyperbola

In mathematics a hyperbola is a smooth function planar curve having two connected components or branches, each a mirror image of the other and resembling two infinite bow aimed at each other....
 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:

It is related to the semi-major axis
Semi-major axis

In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
 through the eccentricity
Eccentricity (mathematics)

In mathematics, the eccentricity, denoted e or , is a parameter associated with every Conic section#Eccentricity. It can be thought of as a measure of how much the conic section deviates from being circular....
, as follows:

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

The conjugate axis of a hyperbola runs in the same direction as the Semi-major axis.