Ellipse Ellipse In mathematics, an Ellipse is closed curve made by the intersection of cone and plane. It is a plane curve. Apollionous has first given the name ellipse and it was first propounded by Euclid. An ellipse can be made by inserting two points in the cardboard and circle of string around these two pins, then putting the pencil in the loop and pulling it as far as possible in all directions, while taking care that the string does not break. A circle comes under the special cases of ellipse. Like circle ellipse also has the point at centre which is known as focus. But ellipse has foci (plural of focus) which generate a line many times these foci is known as generator lines, and the other name of these two generator lines is genetarix. Ellipse has the oval shape. In the early sixteen century, a mathematician named, Kepler said that the mars orbit is in the shape of oval and later he noticed that it make the shape of ellipse with the sun at the focus.
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We can represent ellipse by the equation x = a cos theta and y = b sin theta where x and y are the rectangular coordinates considering any point of the ellipse, where parameter theta is the angle in the center measured from x- axis counter clockwise. This method of drawing an ellipse is known as concentric circle method. The result of projecting a circle, sphere or an ellipse three dimensionally on to a plane by using parallel lines is an ellipse. We can also define ellipse as the set of point s which are at the same distance from any one focus and from any one particular circle forming the directrix, which is centered on the other focus. The distance between the center of the circle and the focus is the radius of the directrix circle and thus the focus insidethe directrix circle is the ellipse. The things which are in the shape of ellipse, a particular name is specified for them which is known as elliptical. Now let’s understand the few terms which form the relation with the ellipse. The major axis of the ellipse is its longest diameter and the minor axis is its shortest diameter. Like circle the perimeter of circle is also known as circumference. . Chord is the term used for the line segment which is linking any two points on ellipse. A tangent line is the line passing through the an ellipse touching any one point. As we have already discussed above that circle comes under the special case of ellipse.
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If we consider the both generator lines of the same size then the close figure form will be of circle. Therefore now we can also explain the ellipse using its formula. The origin of the ellipse will be (0,0) and suppose (n) as its horizontal axis and (m) as a its vertical axis and its coordinates are (x,y) so the formula generate will be x2
---- + ----- = 1. n2
Ellipse has its applications in many fields such as in non-circular gears, in optics, in statistics and finance, in computer and in optimization theory.
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