Elliptical Segment Calculator. An axis-aligned ellipse centered at the origin with a>b. Elliptical Sector Calculator. Enter both semi axes and two of the three angles Θ 1, Θ 2 and θ. It helps a lot with geometry, but also useful for science. The area bounded by the ellipse is ˇab. Calculations at an elliptical sector. 2 Area of an Ellipse An axis-aligned ellipse centered at the origin is x a 2 + y b 2 = 1 (1) where I assume that a>b, in which case the major axis is along the x-axis. An elliptical sector is formed by an ellipse and an angle originating at its center. Figure1shows such an ellipse. ½ab =½ab arccos(x/a).. One focus, two foci. Let C be the ellipse with equation x /a +y /b =1, with a>b, and let F,F'=(±,0) be its foci (see Figure 7.1.2).. A parametric representation for C is given by (a cos , b sin ).The area of the shaded sector below is . The foci always lie on the major (longest) axis, spaced equally each side of the center. The distance from any point M on the ellipse to the focus F is a constant fraction of that points perpendicular distance to the directrix, resulting in the equality p/e. areasolver.zip: 7k: 04-03-03: Area Solver Features: This is a simple area solving program that I wrote about two years ago. These 2 foci are fixed and never move. Sector area formula The formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2: You may, very rarely, hear about the sector of an ellipse, but the formulas are way, way more difficult to use than the circle sector area equations. The word foci (pronounced 'foe-sigh') is the plural of 'focus'. The focus points for the ellipse are at F 1 and F 2. Figure 1. Two points, A and B, are on the ellipse shown above. Directrix of ellipse (1 - k) is a line parallel to the minor axis and no touch to the ellipse. Now, the ellipse itself is a new set of points. Area of a Sector Simply finds the area of a sector for a given circle. An ellipse has two focus points. Choose the number of decimal places. If the major axis and minor axis are the same length, the figure is a circle and both foci are at the center. Mathematically, an ellipse is a 2D closed curve where the sum of the distances between any point on it and two fixed points, called the focus points (foci for plural) is the same. You can always add and subtract some triangles from the sections based on the center to get a sector based on the foci. Instead of having all points the same distance from the center point, though, an ellipse is shaped so that when you add together the distances from two points inside the ellipse (called the foci) they always add up to the same number. For example, looking at the picture in the question, and shaded section on the right. In the demonstration below, these foci are represented by blue tacks . 7.3 Additional Properties of Ellipses. 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