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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.
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When is an ellipse very accentrie?
An ellipse is very eccentric when its foci are far apart.The closer one focus is to the other, the less eccentric the ellipse is.When when both foci are the same point, the eccentricity is zero, and the ellipse is a circle.
What happen as foci of an ellipse get closer together?
The ellipse will become more circular until it becomes a circle when the two foci coincide.
What is the difference between a circle and a ellipse?
Basically a circle has a constant radius throughout and an ellipse does not.a circle has a constant radiusan ellipse has two foci. they are at either end of the ellipse
What is the limiting case of ellipse?
The "limiting case" of the ellipse can be a circle, or it can be a straight line.This isn't a Health question; this is a Math question: specifically, a Geometry question.Definitions: An ellipse is an 'O' shape, like the slice of an egg.A "limiting case" is an extreme case, one extreme or the other.The extreme case of an ellipse, which some people call the "limiting case" of the ellipse, can be a circle, or it can be a straight line. Without going too deeply into the math, when you stretch it out enough, an ellipse tends to become a straight line. When you "round it out", the ellipse tends to look like a circle.An ellipse is also a conic section: that is, a cut or a slice that you make into a cone. As you make more and more extreme cuts, you get either a circle, or a straight line.A nice picture of an ellipse, and a good brief explanation, is at Math Warehouse: An ellipse is the locus of all points of the plane, the sum of whose distances to two fixed points add to the same constant. Each fixed point is called a focus. The two fixed points are called the focuses, or foci, the plural of focus.When the two fixed points of an ellipse are the same point, you get a circle. [Imagine the two points getting closer and closer together, until they become the same point: then, you get a circle. A circle is just a special case of an ellipse.]If the two focuses get infinitely farther apart, you get a straight line.Another way of saying this is:When the eccentricity of an ellipse is zero, the ellipse is a circle. When the eccentricity approaches one, you tend to get a straight line. {Note: if you want to get picky, you never really get to a straight line (that's the infinite case); you just approximate a straight line.}The equation for an ellipse is PF1 + PF2 = 2aThis is the line segment definition of an ellipse, where PF1 and PF2 are the line segments, which equal the distances from a point P to Focus 1 and Focus 2.Math Warehouse says the same thing, slightly differently: An ellipse is the set of all points in a plane such that the sum of the distances from T to two fixed points F1 and F2 is a given constant, K. The trigonometric (sine, cosine) and coordinate-geometry (x,y) definitions for an ellipse are at the Math Open Reference siteOther ellipse definitionsThere are other ways to define an ellipse. Both use coordinate geometry.Using Trigonometry, with two equations: x = a cos(t)y = b sin(t)where t is the parameter and a is the horizontal semi-axis and b the vertical semi-axisUsing the formula x2/a2 + y2/b2 = 1Where a is the horizontal semi-axis and b the vertical semi-axis and the origin is the ellipse center point.See also:conic sectionsThe circle is a limiting case of the ellipse, when the slice is made at right angles to the axis, while the parabola is the limiting case of both the ...http://www.daviddarling.info/encyclopedia/C/conic.html - CachedChallenge question about ellipse and circles? - Yahoo! UK ...The limiting case occurs when the radius of curvature of the ellipse is equal to that of the circle. For a smaller radius of curvature, a circle tangent at ...Degenerate Ellipse - MAAAs long as r is positive, the resulting curve is a legitimate ellipse. In the limiting case of r = 0, the circle is collapsed to a line segment. ...
How does average change help find instant rate of change in math?
This is done with a process of limits. Average rate of change is, for example, (change of y) / (change of x). If you make "change of x" smaller and smaller, in theory (with certain assumptions, a bit too technical to mention here), you get closer and closer to the instant rate of change. In the "limit", when "change of x" approaches zero, you get the true instantaneous rate of change.
If the pins in the following diagram were placed closer together the eccentricity of the ellipse being constructed would?
Assuming that the pins represent the foci, the answer is that the eccentricity would be reduced.
The ellipse with less eccentric is smaller or larger than an ellipse with more eccentric?
An ellipse with less eccentricity will be closer in shape to a circle, so it will generally be smaller than an ellipse with more eccentricity which is more elongated. The size comparison also depends on the specific dimensions of the ellipses.
When the pins are closer together the eccentricity?
When the pins are closer together, the eccentricity of the system decreases. Eccentricity refers to how off-center an object is relative to its axis of rotation, and when the pins are closer together, the object rotates in a more centered manner, reducing the eccentricity.
How does the eccentricity of an ellipse relates to its shape?
The eccentricity of an ellipse, denoted as ( e ), is a measure of how much the ellipse deviates from being circular. It ranges from 0 (a perfect circle) to values approaching 1 (which represents a highly elongated shape). A lower eccentricity indicates a shape closer to a circle, while a higher eccentricity reflects a more elongated or stretched appearance. Thus, the eccentricity directly influences the overall shape and visual characteristics of the ellipse.
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.
When is an ellipse very accentrie?
An ellipse is very eccentric when its foci are far apart.The closer one focus is to the other, the less eccentric the ellipse is.When when both foci are the same point, the eccentricity is zero, and the ellipse is a circle.
How does numerical value of e change as shape of ellipse approaches straight line?
"e" will get greater. The eccentricity for a line is one and for a circle is zero. Since it is getting closer to becoming a line it will go up in value. ; ) "e" will get greater. The eccentricity for a line is one and for a circle is zero. Since it is getting closer to becoming a line it will go up in value. ; )
What happens to the shape of an ellipse as the foci are moved closer together?
As the foci of an ellipse move closer together, the ellipse becomes more circular in shape. When the foci coincide, the shape is a circle. Note that circles are a subset of ellipses.
What happen as foci of an ellipse get closer together?
The ellipse will become more circular until it becomes a circle when the two foci coincide.
Are some elliptical orbits more circular than others?
Yes, some elliptical orbits are more circular than others. An ellipse has two main characteristics - its eccentricity and its semi-major axis. The closer the eccentricity is to 0, the more circular the orbit is.
What is the difference between circle and ellipse?
The simple answer is that an ellipse is a squashed circle.A more precise answer is that an ellipse is the locus (a collection) of points such that the sum of their distances from two fixed points (called foci) remains a constant. A circle is the locus of points that are all the same distance from a fixed point. If the two foci are moved closer together, the ellipse becomes more and more like a circle and finally, when they coincide, the ellipse becomes a circle. So, a circle is a special case of an ellipse.
How can one determine the eccentricity of an object or orbit?
The eccentricity of an object or orbit can be determined by calculating the ratio of the distance between the foci of the ellipse to the length of the major axis. This value ranges from 0 (perfect circle) to 1 (highly elongated ellipse).
