WHAT ARE THE ELEMENTS OF THE PARABLE? (PARTS) - MATHS - 2025

The parabola elements are the axis, the focus, the directrix, the parameter, the vertex, the focal length, the chord, the focal chord, the straight side and its points.

Thanks to these elements or parts, lengths and properties of the parabolas can be calculated. The main components from which all other elements arise are the axis, the directrix, and the focus.

Some of the elements of a parable. Image modified from Drini / CC BY-SA (http://creativecommons.org/licenses/by-sa/3.0/)

A parabola is a curved line whose points are equidistant to a focus located on the inside of the curve, and to a line called a directrix, located on the outside and perpendicular to the parabola. Geometrically it corresponds to a conic section with eccentricity equal to 1.

The elements that make up a parabola

Since all the parabolas correspond to a conic section with the same eccentricity, at the geometric level all the parabolas are similar, and the only difference between one and the other is the scale with which they work.

Normally during the study of mathematics, physics and geometry, parabolas are usually drawn by hand without taking into account some parameters. For this reason, most parabolas appear to have a different shape or angle.

The three main elements that make up a parabola are the focus, the axis and the directrix. The axis and the directrix are perpendicular lines that intersect while the focus is a point on the axis.

The parabola constitutes a curved line between the focus and the directrix, all the points of the parabola are equidistant from the focus and the directrix.

1- Focus

It is a point located on the axis, any point of the parabola is at the same distance from the focus and the directrix.

2- Axis

It is the symmetric axis of the parabola, the point where the axis intersects the parabola is called the vertex.

3- Guideline

The directrix is ​​a line perpendicular to the axis that opposes the parabola. If you are at any point on the parabola to draw a line to the focus, the length of this will be equal to a line drawn to the directrix.

4- Parameter

It is a line perpendicular to the directrix and parallel to the axis that forms a vector between the focus and the directrix.

5- Vertex

It corresponds to the point of intersection where the axis and the parabola intersect. The vertex of a parabola is at the midpoint between the focus and the directrix.

6- Focal length

It is the distance between the focus and the vertex. It is equivalent to the value of the parameter divided by 2.

7- Rope

A chord is any straight line that connects 2 points of a parabola.

8- Focal cord

It is a chord that joins 2 points of a parabola passing through the focus.

9- Straight side

The straight side is a focal chord parallel to the directrix and perpendicular to the axis. Its value is twice the parameter.

10 points

When drawing a parabola, 2 quite differentiable spaces are visually formed on both sides of the curve. These 2 sides make up the inner and outer points of the parabola.

Interior points are all those located on the internal side of the curve. The outer points are those located in the outer part, between the parabola and the directrix.

References

1. Parabola (nd). Retrieved on December 10, 2017, from Mathwords.
2. Definition and elements of the parabola (nd). Retrieved on December 10, 2017, from Sangakoo.
3. Parabola (nd). Retrieved on December 10, 2017, from Vitutor.
4. Elements of a parabola (nd). Retrieved on December 10, 2017, from Universo Fórmula.
5. Parabola (nd). Retrieved on December 10, 2017, from Math is fun.