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Parabola and Focus

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    A parabola is a planar. mirror-symmetrical curve. which is about U-shaped when oriented as shown in the diagram. but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to specify curves of precisely the same form.

    One description of a parabola involves a point ( the focal point ) and a line ( the directrix ) . The focal point does non lie on the directrix. The venue of points in that plane that are equidistant from both the directrix and the focal point is the parabola. Another description of a parabola is as a conelike subdivision. created from the intersection of a right round conelike surface and a planewhich is parallel to another plane which is digressive to the conelike surface. [ a ] A 3rd description is algebraic. A parabola is a graph of a quadratic map. such as

    The line perpendicular to the directrix and passing through the focal point ( that is. the line that splits the parabola through the center ) is called the “axis of symmetry” . The point on the axis of symmetricalness that intersects the parabola is called the “vertex” . and it is the point where the curvature is greatest. The distance between the vertex and the focal point. measured along the axis of symmetricalness. is the “focal length” . The “latus rectum” is the chord of the parabola which is parallel to the directrix and base on ballss through the focal point. Parabolas can open up. down. left. right. or in some other arbitrary way. Any parabola can be repositioned and rescaled to suit precisely on any other parabola — that is. all parabolas are geometrically similar.

    Parabolas have the belongings that. if they are made of stuff that reflects visible radiation. so light which enters a parabola going parallel to its axis of symmetricalness is reflected to its focal point. regardless of where on the parabola the contemplation occurs. Conversely. visible radiation that originates from a point beginning at the focal point is reflected ( “collimated” ) into a parallel beam. go forthing the parabola analogue to the axis of symmetricalness. The same effects occur with sound and other signifiers of energy. This brooding belongings is the footing of many practical utilizations of parabolas.

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