Semiminor axis
In geometry, the semiminor 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 semimajor 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.
Contents
 Ellipse 1
 Hyperbola 2
 References 3
 External links 4
Ellipse
The semiminor 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 semiminor 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 semiminor axis b is related to the semimajor axis a through the eccentricity e and the semilatus rectum l, as follows:
 b = a \sqrt{1e^2}\,\!
 al=b^2\,\!.
The semiminor 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 semiminor 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 semiminor axis, of length b. Denoting the semimajor axis length (distance from the center to a vertex) as a, the semiminor and semimajor 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 semiminor axis and the semimajor axis are related through the eccentricity, as follows:
 b = a \sqrt{e^21}.
Note that in a hyperbola b can be larger than a. [2]
References
 ^ http://www.mathopenref.com/ellipseaxes.html,"Major / Minor axis of an ellipse",Math Open Reference, 12 May 2013
External links
 Semiminor and semimajor axes of an ellipse With interactive animation
