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
In optics an aberration is a defect in the image formed by a lens or curved mirror. In chromatic
aberration the image formed by a lens, but not a mirror, has coloured fringes as a result of the different extent to which light of different colours is refracted by glass. It is corrected by using an achromaticlens. In spherical aberration, the rays from the object come to a focus in slightly different positions as a result of the curvature of the lens or mirror. For a mirror receiving light strictly parallel with its axis, this can be corrected by using a parabolic surface rather than a spherical surface. Spherical aberration in lenses is minimized by making both surfaces contribute equally to the ray deviations, and can (though with reduced image brightness) be reduced by the use of diaphragms to let light pass only through the centre part of the lens. In astronomy an aberration is the apparentdisplacement in the position of a star as a result of the earth's motion round the sun. Light appears to come from a point that is slightly displaced in the direction of the earth's motion. The angular displacement a = v/c, where v is the earth's orbitalvelocity and c is the speed of light. Aberration was discovered in 1728 by the English astronomer James Bradley and was the first observational proof that the Earth orbits the Sun.
In astronomy, aberration is a small periodical change of the position in the stars and other heavenly bodies, due to the combined effect of the motion of light and the motion of the observer; this is called annual aberration, when the observer's motion is that of the earth in its orbit, and daily or diurnal aberration, when of the earth on its axis; amounting when greatest, in the former case, to 20.4', and in the latter, to 0.3'. Planetary aberration is that due to the motion of light and the motion of the planet relative to the earth. In optics, aberration is the convergence to different foci, by a lens or mirror, of rays of light emanating from one and the same point, or the deviation of such rays from a single focus; called spherical aberration, when due to the spherical form of the lens or mirror, such form giving different foci for central and marginal rays; and chromatic aberration, when due to different refrangibilities of the coloured rays of the spectrum, those of each colour having a distinct focus. Research Aberration
An ellipse is a figure in geometry ranking next in importance to the circle, and produced when any cone is cut by a plane which passes through it not parallel to nor cutting the base. Kepler discovered that the paths described by the planets in their revolutions round the sun are ellipses, the sun being placed in one of the foci. To describe an ellipse: At a given distance"on the surface on which the ellipse is to be described fix two pins, and pass a looped string round them. Keep the string stretched by a pencil, and move the pencil round, keeping the string at the same tension, then the ellipse will be described. A line drawn from any point in the curve perpendicularly to the axis is an ordinate to the axis. Any straight line drawn through the centre and terminated both ways by the curve is called a diameter. Research Ellipse
In optics, the focus is a point in which any number of rays of light meet after being reflected or refracted by a mirror or a lens.
In geometry, the focus is an important point on the principal axis of the parabola, ellipse, and hyperbola. The ellipse and hyperbola have each two foci, the parabola one, though in the latter case we may suppose a second focus at an infinite distance. The foci were so called from the fact that rays of light proceeding from one focus and reflected from a corresponding reflecting surf ace pass through the other focus. Research Focus
Abbreviations
Research Hyperbola
