A hyperbola is a plane curve, one of the conic sections, formed by a plane that cuts both nappes of a right circular cone but does not pass through the vertex of the cone. A hyperbola has two U- shaped non-intersecting branches, identical in form, with the open parts facing in opposite directions; the arms of each branch separate as they recede. A hyperbola is also defined as the locus of all points, such that the difference between the distances from any point on the hyperbola to two fixed points, called the foci, is equal to a constant. Each branch contains one focus in its interior area; the line joining the foci intersects each branch in a point called a vertex. This line, or the segment between the vertices, is called the transverse axis. The line perpendicular to the transverse axis and passing through the point midway between the vertices, midway between the foci, is the conjugate axis. The two axes meet at the centre of the hyperbola, which is symmetric with respect to each axis and the centre.
A hyperbola has two asymptotes passing through the centre; an asymptote of a curve is a straight line with the property that the distance between it and the curve approaches zero as the curve recedes to infinity. A rectangular or equilateral hyperbola has asymptotes that are perpendicular to each other. The hyperbola has useful and important properties. In particular, the angle formed at a point on the hyperbola by the lines joining the point to the foci is bisected by the tangent to the hyperbola at that point. In astronomy, some orbits are hyperbolic in shape. The modern navigational device the loran also uses
hyperbolas. Research Hyperbola
The Probert Encyclopaedia was designed, edited and programed by
Matt and Leela Probert
Abbreviations
General Information
Research Hyperbola
