Semi-minor axis - Citizendia

The semi minor axis of an ellipse

In geometry, the semi-minor axis (also semiminor axis) is a line segment associated with most conic sections (that is, with ellipses and hyperbolas). Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position In Geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its end points In Mathematics, a conic section (or just conic) is a Curve obtained by intersecting a cone (more precisely a circular Conical surface One end of the segment is the center of the conic section, and it is at right angles with the semi-major axis. In Geometry and Trigonometry, a right angle is an angle of 90 degrees corresponding to a quarter turn (that is a quarter of a full circle In Geometry, the semi-major axis (also semimajor 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. Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is Symmetry with respect

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. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a In Geometry, the foci (singular focus) are a pair of special points used in describing Conic sections The four types of conic sections are the Circle 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:

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

$al=b^2\,\!$ . In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae In Mathematics, the eccentricity, denoted e or \varepsilon is a parameter associated with every conic section. In Mathematics, a conic section (or just conic) is a Curve obtained by intersecting a cone (more precisely a circular Conical surface

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. In Mathematics, the parabola (pəˈræbələ from the Greek παραβολή) is a Conic section, the intersection of a right circular Thus a and b tend to infinity, a faster than b.

External links

Semi-minor and semi-major axes of an ellipse With interactive animation

Hyperbola

The length of 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. In Geometry, a hyperbola ( Greek, "over-thrown" has several equivalent definitions In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae In Mathematics, the eccentricity, denoted e or \varepsilon is a parameter associated with every conic section.

The conjugate axis of a hyperbola runs in the same direction as the Semi-major axis. [1]

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