Ellipse area formula: S=π (pi) ×a×b, where a and b are the lengths of the major axis and minor axis of the ellipse respectively. The ellipse area formula belongs to the field of geometric mathematics.

1. What is an ellipse? -Definition of ellipse

We call the locus of a point whose sum of the distances from a point to two fixed points on a plane is constant (greater than the distance between the two fixed points) an ellipse. These two fixed points are called the focal points of the ellipse, the distance between the two focal points is called the focal length of the ellipse, and half of the focal length is called the half focal length.

Second, the standard equation of ellipse

We call the equation of an ellipse with the center of symmetry at the origin of the plane rectangular coordinate system and two focal points on the same coordinate axis the standard equation of ellipse.

The standard equation of ellipse has two forms: "the focus is on the X axis" and "the focus is on the Y axis". The comparison of these two forms of standard equations and their characteristics is shown in the figure.

Third, the major axis and minor axis of the ellipse.

If the line segment corresponding to the arbitrary symmetry axis of the ellipse and the two intersections of the ellipse is called the axis of the ellipse, then the long axis is called the long axis of the ellipse, and the short axis is called the short axis of the ellipse.

4. Formulas for the major and minor axes and areas of an ellipse.

Traditionally, the length of the long axis of an ellipse is recorded as "2a", and half of the long axis with the center of ellipse symmetry as the endpoint is called the long semi-axis of the ellipse; Write down the length of the short axis of the ellipse as "2b", and call half of the short axis with the center of ellipse symmetry as the semi-axis of the ellipse.

With the concepts of "long semi-axis" and "short semi-axis", the area formula of any ellipse can be expressed as: "the area of an ellipse is equal to π, the product of long semi-axis and short semi-axis", which can be expressed as: S=πab through mathematical formula.