Formula of Eccentricity of Hyperbola
The formula to find eccentricity of a hyperbola is written as follows,
e = c/a
where,
e = eccentricity of hyperbola,
c = distance between a point on hyperbola and its focus,
a = distance between the same point and directrix of the hyperbola.
x2/a2 – y2/b2 = 1
Formula for eccentricity is written as,
e = √(1 + b2/a2)
where,
e = eccentricity of the hyperbola,
a = length of major axis of the hyperbola,
b = length of minor axis of the hyperbola.
From the above formula, we see that eccentricity of a hyperbola depends on the length of major axis and that of minor axis of the hyperbola.
Eccentricity of Hyperbola
Eccentricity of Hyperbola refers to the deviation of the conic section from being circular and closeness towards being oval in shape. In other words, it can be defined as the measure of how flattened or elongated a hyperbola is. It is calculated as the ratio of the distance of a point on the hyperbola from its focus and the directrix. This ratio for a hyperbola is always greater than one, which implies that the two branches of the hyperbola diverge away from each other when extended to infinity. It is denoted by the letter ‘e’. It can be used to predict the shape of the hyperbola.
In this article, we will discuss, the eccentricity of a hyperbola, its formula, derivation, solved examples, practice problems and related frequently asked questions.
Table of Content
- What is the Eccentricity of Hyperbola?
- Formula of Eccentricity of Hyperbola
- Diagram of Hyperbola
- Derivation of Eccentricity of Hyperbola
- Solved Examples – Eccentricity of Hyperbola
- Practice Problems – Eccentricity of Hyperbola
- FAQs – Eccentricity of Hyperbola