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.