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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 = 2a
This 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 definitions
There 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-axis
- Using the formula x2/a2 + y2/b2 = 1
Where a is the horizontal semi-axis and b the vertical semi-axis and the origin is the ellipse center point.
See also:
conic sections
The 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 - Cached
Challenge 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 - MAA
As 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. ...
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How do you find the surface area of an ellipse?
An ellipse is a two dimensional shape, so it does not have a "surface area", only an "area". Any ellipse has two radii, the major one and the minor one. We'll call them R1 and R2. The area of the ellipse then can be calculated with the function: a = πR1R2 You will notice that this is the same equation as the area for a circle. The circle is a special case though, because it is an ellipse in which both axes are the same length. In that case, R1 equals R2, so we can simply call it r and say: a = πr2
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
Can the foci's of and ellipse be outside the ellipse?
No.
Derive normal distribution as a limiting case of binomial distribution?
ref veeru
What are the six conic sections?
A conic section is the intersection of a plane and a cone. By changing the angle and location of intersection, we can produce a circle, ellipse, parabola or hyperbola; or in the special case when the plane touches the vertex: a point, line or 2 intersecting lines.Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it is sometimes called the fourth type of conic section.
Which is the limiting case of ellipse?
circle
What conic sections describes a closed curve?
An ellipse is a conic section which is a closed curve. A circle is a special case of an ellipse.
Is every circle an ellipse?
Yes; the circle is a special case of an ellipse.
What is the FOCI of a circle?
A circle is an ellipse with an eccentricity of zero. Both foci of that ellipse are at the same point. In the special case of the circle, that point is called the "center".
What is earth orbit of the sun?
Earth orbits the Sun in an ellipse; the Sun is in one of the ellipse's focal points. The ellipse's shape, in this case, is quite close to a circle. The average distance from Earth to Sun is about 150 million kilometers.
How the limiting reactant control the product?
The yield of the reaction depends in this case only on the concentration of the limiting reactant.
How do you find the surface area of an ellipse?
An ellipse is a two dimensional shape, so it does not have a "surface area", only an "area". Any ellipse has two radii, the major one and the minor one. We'll call them R1 and R2. The area of the ellipse then can be calculated with the function: a = πR1R2 You will notice that this is the same equation as the area for a circle. The circle is a special case though, because it is an ellipse in which both axes are the same length. In that case, R1 equals R2, so we can simply call it r and say: a = πr2
What does the shape of an ellipse describe to us?
The path of an object in orbit around another object. It's a "conical section", shaped like a circle, but "flattened" in one direction (a circle can be considered a special case of an ellipse). An ellipse has two focal points.
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 orbit of the earth and moon like?
The orbits of any object orbiting any other object is an ellipse. The central object (the Sun, in the case of the Earth) is in one of the focal points of the ellipse.
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 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.
