Hyperbola
Chapter Name : Conic Section |
Sub Topic Code : 104_11_11_06_02 |
Topic Name : Hyperbola |
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Sub Topic Name : Eccentricity |
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Introduction
• For hyperbola eccentricity is always greater than 1 as the distance between the foci is always greater than the distance between its vertices. • As eccentricity increases from 0 to infinity, the nature of curve changes from a circle to a straight line with ellipse, parabola and hyperbola in transition.
Pre-Requisites:
Linear Equation, Quadratic Equation, Basic coordinate geometry, Equation of line
Real Life Question:
What is the eccentricity of hyperbola?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Hyperbola | A hyperbola is defined as the locus of points where the absolute value of the difference of the distances to the two foci is a constant. |
| Focus | The fixed points are known as foci (plural of focus). |
| Directrix | Directrix of hyperbola is a line such that ratio of the distance of the points on the hyperbola from focus to its distance from directrix is constant. |
| Eccentricity | The ratio of the distance of any point on a conic section from a focus to its distance from the corresponding directrix. |
Learning aids / Gadgets
| Gadgets | How it can be used |
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Real life uses :
It is used widely in architecture, civil engineering and space shuttle launching. Many shapes and designs are made using the concepts of hyperbola. Hyperbolic path is used for launching of several satellites.
Practical examples around us
| Examples | Explainations |
|---|---|
| Hour glass | If you notice the outline of the hourglass it forms the exact shape of a hyperbola. |
| Base Ball | If you look closely you can see how the stitches in this baseball form a hyperbola. |
What you learn in Theory:
What is eccentricity of hyperbola?