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What happens when you increase the distance between two foci?
-- If they're the foci of a single optical system, then the result can't be stated in general.It depends on the curvatures and relative position of the lenses.-- If they're both the foci of the same ellipse, then the ellipse becomes more eccentric.That is, more squashed and less circular.-- If they're the foci of two parabolas, then there's no relationship between them, andnothing in particular depends on the distance between them.The answer depends on whether they are the foci of an ellipse or a hyperbola.
What is the difference between a circle and an ellipse?
-- the eccentricity or -- the distance between the foci or -- the ratio of the major and minor axes
How does the eccentricity of an ellipse change as the foci get closer together?
As the foci of an ellipse move closer together, the eccentricity of the ellipse decreases. Eccentricity is a measure of how elongated the ellipse is, defined as the ratio of the distance between the foci to the length of the major axis. When the foci are closer, the ellipse becomes more circular, resulting in a lower eccentricity value, approaching zero as the foci converge to a single point.
What is foci?
Foci, (the plural of focus), are a pair of points used in determining conic sections. They always fall on the major axis of symmetry of a conic. For example, in a circle, there is only one focus, the centerpoint. Every distance from the focus to any other point on the circle will be the same. In a parabola, the distance from any point of the parabola to the focus equals the distance from the centerpoint to the directrix. In a hyperbola, the difference of the distances between a point on the hyperbola and the focus points will be constant, and in an ellipse, the sum of the distances from any point on the ellipse to one of the foci is constant.
What is foci of hyperbola?
A half of a hyperbola is defined as the locus of points such that the distance of the point from one fixed point (a focus) and its distance from a fixed line (the directrix) is a constant that is greater than 1 (the eccentricity). By symmetry, a hyperbola has two foci and two directrices.
