Ellipses are formed by the set of all points, which have a sum of distances from two fixed points that is constant. The two fixed points are called the foci of the ellipse. The foci are surrounded by a curve that has an oval shape. Some of the most important parts of ellipses are the center, the foci, the vertices, the major axis, and the minor axis.
Here, we will learn more details of the parts of the ellipse along with diagrams to illustrate the concepts. In addition, we will learn how to calculate the area of ellipses using the length of the semi-major axis and the length of the semi-minor axis.
What are ellipses?
Ellipses are the set of all points in the Cartesian plane, which have a sum of distances from two fixed points that is equal to a constant. The fixed points are called the foci of the ellipse.
We can also define ellipses as conic sections that are formed by cutting a cone with a plane. For the ellipse to be formed, the plane must be inclined at an angle to the base of the cone.
Important parts of an ellipse
The following are the most important parts of an ellipse:
- Major axis
- Minor axis
- Focal length
- Semi-minor axis
- Semi-major axis
Ellipses have two foci, which are fixed points that are located on the major axis. Along with the vertices, the foci are used to define the ellipses. The foci can be denoted by the letter F.
The axes are lines of symmetry of the ellipse. The axes are segments that extend from one side of the ellipse to the other side through the center. Therefore, the axes are diameters and the major axis is the longest diameter of the ellipse.
The length of the major axis is equivalent to the sum of the lengths from any point on the ellipse to the two foci.
The minor axis is perpendicular to the major axis. This axis is the shortest diameter of the ellipse. The minor axis cuts the major axis into two equal parts.
The center of the ellipse is located at the intersection of the major axis and the minor axis. Ellipses can have a center at the origin (0, 0) or a center at any other point (h, k).
The focal length is the length of the segment that extends from one focus to the other.
The vertices are the endpoints of the major axis. These points represent the intersection between the major axis and the ellipse.
The covertices are the endpoints of the minor axis. These points represent the intersection between the minor axis and the ellipse.
The semi-major axis represents the segment that extends from the center to a vertex of the ellipse. The semi-major axis passes through one of the foci and is exactly half of the major axis.
The semi-minor axis is the segment perpendicular to the semi-major axis. The semi-minor axis extends from the center to the covertex and is exactly half of the minor axis.
How to find the area of an ellipse?
The area of any ellipse can be calculated using the lengths of the semi-major axis and the semi-minor axis. Therefore, we use the following formula:
Area =$latex \pi ab$
- a is the length of the semi-major axis
- b is the length of the semi-minor axis
Interested in learning more about ellipses? Take a look at these pages: