Focus (geometry)

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, parabola, ellipse, and hyperbola.The focus has two equivalent defining properties; and they always fall on the major axis of symmetry of the conic. The simpler depends on the type of conic:In an ellipse, the sum of the distances from any point on the ellipse to the two foci is a constant (which is always the length of the major axis of the ellipse).In a circle, there is only one focus, the center of the circle, and all the points of the circle are equidistant from it. (This can be viewed a special case of the above, with a circle being an ellipse with two foci at the same point; the sum of the distances is the diameter.) In a hyperbola, the difference of the distances is always constant.A parabola also only has one focus (although it is sometimes useful to speak of a focus at infinity); but there is a line called the directrix such that the distance from any point of the parabola to the focus is equal to the (perpendicular) distance from the point to the directrix.
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