Definition and elements of the parabola

A parabola is defined by the set of the points of the plane that are equidistant to a fixed straight line and a fixed point: $$$d(P,D)=d(P,F)$$$

Elements of the parabola


  • Focus: It is the fixed point $$F$$.

  • Generator line: It is the fixed straight line $$D$$.

  • Parameter: The distance between the focus and the generator line of a parabola is called the parameter $$p$$.

  • Axis: The straight line perpendicular to the generator that goes through the focus is called axis. It is the axis of symmetry of the parabola.

  • Vertex: It is the middle point between the focus and the generator line. Also, it is possible to consider it the point of intersection of the axis with the parabola.

  • Radius vector: It is the segment that joins any point of the parabola with the focus.