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-- 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, and

nothing in particular depends on the distance between them.

The answer depends on whether they are the foci of an ellipse or a hyperbola.

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-- 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, and

nothing in particular depends on the distance between them.

Q: What happens when you increase the distance between two foci?

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The answer depends on whether they are the foci of an ellipse or a hyperbola.

-- the eccentricity or -- the distance between the foci or -- the ratio of the major and minor axes

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.

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.

The standard equation for an ellipse centered at the origin is [x2/a2] + [y2/b2] = 1 We also have the relationship, b2 = a2 - c2 where c is the distance of the foci from the centre and a & b are the half lengths of the major and minor axes respectively. When the length of the minor axis equals the distance between the two foci then 2b = 2c : b = c. Thus, a2 =b2 + c2 = 2b2 One of the formulae for the eccentricity of an ellipse is, e = √[(a2 - b2)/a2] Thus, e = √[(2b2 - b2) / 2b2] = √½ = 1/√2.

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The answer depends on whether they are the foci of an ellipse or a hyperbola.

the eccentricity will increase.

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As the distance between foci increases the eccentricity increases, or the reverse relationship.

The distance from one of the foci of an ellipse to its center is half the distance between its two foci. It is referred to as the focal distance and is an important parameter in defining the shape and size of the ellipse.

eccentricity = distance between foci ________________ length of major axis

-- the eccentricity or -- the distance between the foci or -- the ratio of the major and minor axes

The distance between the foci of an ellipse is related to its major axis by the formula: Distance between foci = 2 times the square root of (major axis squared minus minor axis squared). If the major axis of comet Halley were scaled down to 15 cm, you would need to know the minor axis length to calculate the distance between the foci.

The foci of an ellipse are points used to define its shape, and the eccentricity of an ellipse is a measure of how "elongated" or stretched out it is. The closer the foci are to each other, the smaller the eccentricity, while the farther apart the foci are, the larger the eccentricity of the ellipse.