Circular segment
-- the eccentricity or -- the distance between the foci or -- the ratio of the major and minor axes
An ellipse is a closed curved shape that resembles a squashed circle. It has two distinct points called foci, and the sum of the distances from any point on the ellipse to the two foci is constant. The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter.
For Ellipse: The 2 circles made using the the ellipse center as their center, and major and minor axis of the ellipse as the dia.For Hyperbola: 2 Circles with centers at the center of symmetry of the hyperbola and dia as the transverse and conjugate axes of the hyperbolaRead more: eccentric-circles
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
Yes.
The center of a circle is called thecenter, in a way it is the focus of the special case of an ellipse which has equal major and semi major axes...
-- the eccentricity or -- the distance between the foci or -- the ratio of the major and minor axes
You know the formula for the area of a circle of radius R. It is Pi*R2. But what about the formula for the area of an ellipse of semi-major axis of length A and semi-minor axis of length B? (These semi-major axes are half the lengths of, respectively, the largest and smallest diameters of the ellipse--- see Figure 1.) For example, the following is a standard equation for such an ellipse centered at the origin: (x2/A2) + (y2/B2) = 1. The area of such an ellipse is Area = Pi * A * B , a very natural generalization of the formula for a circle!
An ellipse is a closed curved shape that resembles a squashed circle. It has two distinct points called foci, and the sum of the distances from any point on the ellipse to the two foci is constant. The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter.
For Ellipse: The 2 circles made using the the ellipse center as their center, and major and minor axis of the ellipse as the dia.For Hyperbola: 2 Circles with centers at the center of symmetry of the hyperbola and dia as the transverse and conjugate axes of the hyperbolaRead more: eccentric-circles
yes
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
Yes.
ellipse are added hyperbola are subtracted
The major axes of an ellipse is its longest diameter. The minor axes, on the other hand, is the shortest diameter.
This equation is equal to the first one because it produces the same results, always. ... TL;DR - The circle equation is what you get when you multiply all terms from the ellipse equation by the radius. x^2/a^2 + y^2/b^2 = 1 is an ellipse equation. Well, a circle has a radius where a and b are the same.
The eccentricity of an ellipse, e, is the ratio of the distance between the foci to the length of the semi-major axis. As e increases from 0 to 1, the ellipse changes from a circle (e = 0) to form a more flat shape until, at e = 1, it is effectively a straight line.