MathsArea of Ellipse – Explanation, Formulas, Solved Examples and FAQs

Area of Ellipse – Explanation, Formulas, Solved Examples and FAQs

Introduction to Area of Ellipse

An ellipse is a plane curve that results from the intersection of a cone with a plane parallel to its side. The plane curve is formed by the points of intersection of the cone’s surface with the plane. The points of intersection are the ellipse’s vertices. The ellipse’s major and minor axes are the lines drawn from the ellipse’s center to its vertices. The ellipse’s eccentricity is a measure of how elongated the ellipse is.

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    Formulas for Ellipse

    There are three standard equations for drawing an ellipse, depending on the relative positions of the foci (where the ellipse is widest).

    1. If the foci are on the same line, the equation is

    x2/a2 + y2/b2 = 1

    2. If the foci are at different points, the equation is

    x2/a2 + y2/b2 = 1
    + c2

    3. If the foci are at the same point, but the major axis is not along the x-axis, the equation is

    x2/a2 + y2/b2 = 1
    – c2

    Major and Minor Axes

    of a Graph

    The major and minor axes of a graph are the two longest perpendicular lines that intersect in the graph’s center. The major axis is the line that contains the graph’s longest point, while the minor axis is the line that contains the graph’s shortest point.

    Special Case of Ellipse in a Circle’s Area

    If an ellipse intersects a circle at two points, the area of the circle is greater than the area of the ellipse.

    Purpose of Calculating Area of Ellipse

    The purpose of calculating the area of an ellipse is to determine the size of the enclosed region.

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