Practice Problems ā Eccentricity of Hyperbola
P1: What would eccentricity value for given hyperbola: x2 ā y2 = 5.
P2: Find the eccentricity for hyperbola represented as x2/81 ā y2/121 = 1.
P3: What is the value of eccentricity for hyperbola given by x2 ā y2 = 1.
P4: A hyperbola lies along X-axis. Length of its major and minor axis is 8 units and 2 units respectively. Find the value of eccentricity for this hyperbola.
P5: The equation of a hyperbola is written as, x2/16 ā y2/b2 = 1. It has eccentricity value as ā3. Find the value of b.
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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 āeā. 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 ā Eccentricity of Hyperbola
- Practice Problems ā Eccentricity of Hyperbola
- FAQs ā Eccentricity of Hyperbola