Define Ellipses Define Ellipses In mathematics , geometry is define as the warehouse of several figures that are expressed through different types of expression. In geometry there is one figure that is define as the Ellipse. According to the definition of ellipse , it is a set of points that are on a plane and sum of the distance from one point to two other fixed points is equal to a constant value. If there is a point p and two fixed points k1 , k2 then according to the ellipse equation it will express as p k1 + p k2 = c here c is describe as a constant value. Here these two fixed points are define as the focal points of the ellipse. Means point k1 and k2 are focal points of ellipse. As we define the ellipse there are basically two axis that are known as major axis and minor axis and these axis are end on the endpoints that are situated on the ellipse and these endpoints on the ellipse are define as the vertices.
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These two major and minor axis are perpendicular to each other means these axis are created 90' angle between them. The mid point on the major axis is called as center of the ellipse. Minor axis also have the end points that are also situated on the ellipse and these end points are called as the co vertices. We can also describe the endpoints as the meeting point or intersection point of the ellipse and major axis and as well as co vertices are define as the intersection point of minor axis and ellipse. We can express the ellipse in for of expression that are standard form of the ellipse as follows: As we know an ellipse is a close two dimensional curve and there are two axis that are different in lengths. x 2 / a 2 + y 2 / b 2 = 1. In the above expression a and b are two axis of the ellipse that are of different lengths in which a is greater in length than b so a is define as the major or semi major axis and b is called as minor or semi minor axis. We can also express ellipse equation in form of major axis and its eccentricity e when the center of the ellipse is same as origin of x – y plane means center of ellipse is the origin of x y plane then expression for ellipse is expressed as e=(1–b2/a2)1/2. when in the x – y plane , x axis shows as a major axis of the ellipse then expression for ellipse is expressed as: f = 1 – b / a, where f is called as flattening.
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There are some other ways to define the ellipse expression as : (x – h) 2 / a 2 + (y – k) 2 / b 2 = 1. In the above expression a and b should always be positive and h , k are real numbers. In the ellipse expression we know that there are two focal points of ellipse that are situated on the axis and one focal point is described as the origin. Some of people define central of ellipse as origin so there are some distance between these oints that are calculated as : c = (a 2 – b 2) 1 / 2 where c define the distance.
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