- The main elements of an ellipse
- 1- Spotlights
- 2- Focal axis
- 3- Secondary shaft
- 4- Center
- 5- Focal length
- 6- Major semi-axis
- 7- Minor semi-axis
- 8- Vector radii
- 9- Vertices
- References
The elements of an ellipse are its axes, semi-axes, vertices, vector radii, foci, and focal length. These allow establishing certain relationships to fully understand the data and geometric characteristics of the figure.
An ellipse is a figure with an oval shape, usually defined as a flattened sphere. The simplest way to understand the geometry of an ellipse is to cut into a cone with an angle greater than zero.
Unlike circles that have an equidistant center, ellipses start from two central foci.
The main elements of an ellipse
In the same way as in a circle, where the center is the same distance from all the points, in the ellipse all the points are at a constant distance from the sum of the length of the point to the two foci.
This is given by the equation d (P, F) + d (P, F ') = 2K, where d (P, F) and d (P, F') represent the distance between a point and the foci (F and F '), and K is a constant, This means that starting from any point on the ellipse, the sum of the distances between that point and the two foci will always be the same.
1- Spotlights
They are the midpoints of the ellipse and the center of all its geometry, since all the other elements of the figure start from them.
The sum of the distances from any point on the ellipse to the foci is always constant, usually denoted by the letters F and F '.
2- Focal axis
Also known as the major axis, it is a horizontal line that crosses the ellipse touching the two foci and forming two vertices. Divide the figure into 2 equal parts.
3- Secondary shaft
The secondary axis or minor axis is a bisector between the foci of the ellipse, so it can be defined as a vertical line that divides the figure in half right at its center.
An angle of 90 degrees is formed between the focal axis and the secondary axis.
4- Center
It is the place where the focal and secondary axes intersect, although it can also be specified as the midpoint between the 2 foci of an ellipse.
5- Focal length
It is the distance between the 2 foci of an ellipse. It is usually denoted as 2C. At the same time, C is the semifocal distance, which goes from one of the foci to the center.
6- Major semi-axis
It corresponds to the distance between the center and one of the sides of the ellipse (vertex) joined with a horizontal straight line.
Its value is the sum of the distances from any point to the foci divided by 2, of the form a = (d1 + d2) / 2, where a is the semi-major axis and d the distance from a point of the ellipse to a focus.
7- Minor semi-axis
The semi-minor axis is the opposite of the semi-major axis. This crosses the ellipse vertically passing through the center and touching the figure at 2 points.
8- Vector radii
They are the lines that join any point with the lights.
9- Vertices
They are the 4 points where the focal and secondary axes intersect with the ellipse.
References
- Ellipse (2011). Retrieved on December 10, 2017, from Math Open Reference.
- Concept and elements of the ellipse (sf). Retrieved on December 10, 2017, from Cecyt.
- Elements of an ellipse (sf). Retrieved on December 10, 2017, from Universo Fórmula.
- Definition and canonical equation of the ellipse (sf). Retrieved on December 10, 2017, from the National Technological University.
- La Elipse (June 27, 2015). Retrieved on December 10, 2017, from Technical Drawing.