Question

What is $\text{'}a\text{'}$ in a parabola?

Answer 1

Parabola:

• A parabola is a set of points that are equidistant from the focus and the directrix.
• The general equation of a parabola opening upwards or downwards is $x^2=\pm 4ay$,where $a$ is the distance from the vertex to the focus or the distance from the vertex to the directrix.

• The general equation of a parabola opening right or left is $y^2=\pm 4ax$, where $a$ is the distance from the vertex to the focus or the distance from the vertex to the directrix.

• The focus and directrix are equidistant from the vertex of the parabola.
• The directrix is a line perpendicular to the axis of the parabola.

Hence, $\text{'}a\text{'}$is the distance between vertex and focus or directrix and vertex.