Derivation of Eccentricity of Parabola
Consider a parabola M with any point P on it. Let F be the parabola’s focus and l be the directrix with a point from them where Pm is perpendicular to l on the directrix.
Parabola can be defined geometrically as the path in which the point P (as P is an arbitrary figure) follows, and its distance from a fixed point F (Focus) is equal to its distance from the directrix l.
Therefore, we have,
PF = PM
By definition, the eccentricity of a parabola that touches an arbitrary point P from the fixed point F and which is simultaneously perpendicular to the directrix is the ratio of the distance from point P to point F and the perpendicular distance of point P to the directrix.
Hence,
e = PF/PM
Since the two distances are equal in the case of a parabola, we have:
e = PF/PM = PF/PF = 1
Therefore, the eccentricity of a parabola is equal to one.
Eccentricity of Parabola
Eccentricity of Parabola is 1.
Eccentricity of a parabola is a measure of its deviation from a perfect circle. It’s a key parameter that describes the shape and behavior of the parabolic curve. Unlike ellipses and hyperbolas, which have eccentricities greater than or equal to 1, a parabola has an eccentricity exactly equal to 1. In this article, we will discuss the eccentricity of a parabola in detail, including it’s value as well as its derivation.