Diagram of Hyperbola

What is the Eccentricity of Hyperbola?

Eccentricity of a Hyperbola can be defined as the measure of flatness or elongation in its shape. Conic sections are locus of points which follow a certain relation between their distances from a fixed point called focus and a fixed line called directrix. Mathematically, eccentricity is the ratio of the distances from a point on hyperbola to the focus and the directrix. Its value ranges from 1 to infinity, i.e. it is always greater than 1. It is denoted by the symbol ‘e’. If the distance between a point on hyperbola and the focus of hyperbola is ‘c’ and that between the same point and directrix of the hyperbola is ‘a’, eccentricity ‘e’ can be written as, e = c/a....

Formula of Eccentricity of Hyperbola

The formula to find eccentricity of a hyperbola is written as follows,...

Diagram of Hyperbola

The curve represented by a hyperbola is shown as follows,...

Derivation of Eccentricity of Hyperbola

Let us see how the above mentioned formula for eccentricity can be derived. We know that, eccentricity of a hyperbola is the ratio of the distances from a point on it to the focus and the directrix. By using this definition, we would derive expression for eccentricity of hyperbola for following equation of the hyperbola,...

Solved Examples – Eccentricity of Hyperbola

Example 1: Find the value for eccentricity of hyperbola represented by the following equation: x2/144 – y2/36 = 1....

Practice Problems – Eccentricity of Hyperbola

P1: What would eccentricity value for given hyperbola: x2 – y2 = 5....

FAQs – Eccentricity of Hyperbola

What shape is defined by a Hyperbola?...