1. Definition: An ellipse is defined as a set of points whose sum of distances from two fixed points is equal to a constant. These two fixed points are called focal points and the constant is called focal length. According to the definition of ellipse, we can know that the length of the long axis is equal to the distance between the two focal points, that is, 2c, where C is half the focal length. The length of the minor axis is equal to the distance from the two focal points to the center of the ellipse, namely 2b, where b is the length of the semi-minor axis.
2. Pythagorean theorem method: an ellipse can be regarded as a special rectangle, in which four corners are right angles. According to Pythagorean theorem, we can calculate the length of major axis and minor axis. First, we need to find the center of the ellipse, and then use Pythagorean theorem to calculate the distance from the center to any point on the ellipse. The maximum of these distances is the length of the major axis, and the minimum is the length of the minor axis.
3. Polar coordinate method: The polar coordinate equation of an ellipse can be expressed as r = p/( 1-e 2cosθ), where r is the distance from the center of the ellipse to the point, p is the length of the semi-major axis, and e is the eccentricity. The value of r can be obtained by solving this equation, and then the length of the long axis and the short axis can be calculated according to the definitions of the long axis and the short axis.
4. Direct measurement method: If the ellipse is an actual object or figure, we can directly measure the length of the major axis and minor axis with a ruler or measuring tool. This method is suitable for simple ovals, such as round or oval biscuits.
It should be noted that the above methods are suitable for general ellipse shapes, and for special ellipses, other methods may be needed to determine the length of major axis and minor axis. In addition, for non-standard elliptical shapes, some corrections or approximate calculations may be needed.