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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
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.
The eccentricity of the ellipse if minor axis is equal to the distance between the foci is Answer is 1 radical 2 how?
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.
How does distance between foci affect eccentricity?
As the distance between foci increases the eccentricity increases, or the reverse relationship.
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 distance from one of the foci of the ellipse from its center?
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.
What is the formula for eccentricity?
eccentricity = distance between foci ________________ length of major axis
What will happen to the eccentricity of an ellipse as the distance between the foci increases?
the eccentricity will increase.
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
What change takes place in the eccentricity of an ellipse when you increase the distance between the foci?
Troll
What changes takes place in the eccentricity of the ellipses when you increase the distance between the foci?
bruh..
What changes take place in the eccentricity of the ellipse when you increase the distance between the foci's?
Troll
What change takes place in the eccentricity of the ellipses when you increase the distance between the foci?
bruh..
If comet Halley's major axis was scaled down to 15 cm how far apart would the foci be?
The major axis of a comet's orbit is the longest diameter of its elliptical orbit. Given that Halley's comet has a major axis of approximately 35.1 AU (Astronomical Units), or about 5.25 x 10^12 cm, scaling it down to 15 cm would result in a significant reduction in size. To determine the new distance between the foci, we can use the formula for the distance between the foci of an ellipse, which is 2a - 2c, where "a" is half the length of the major axis and "c" is the distance from the center to each focus. With the major axis scaled down to 15 cm, we would have a new major axis of 15 cm / (5.25 x 10^12 cm) = 2.86 x 10^-12 times the original size. Therefore, the distance between the foci would also be scaled down by the same factor, resulting in a new distance of approximately 5.7 x 10^-12 cm.
How are foci related to eccentricity?
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.
