Shape Shape Shape Shape
Hyperbola
Chapter Name : Conic Section
Sub Topic Code : 104_11_11_06_01
Topic Name : Hyperbola
Sub Topic Name : Hyperbola
Introduction

• When you cut a cone such that cutting plane is inclined at an angle greater than the exterior angle of the cone then, the section gives a 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.

Pre-Requisites:

Linear Equation, Quadratic Equation, Basic coordinate geometry, Equation of line

Real Life Question:

What is the section of cone called that is formed when the cutting plane doesn’t intersect the axis of cone inside the cone?

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.
Learning aids / Gadgets
Gadgets How it can be used
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 hyperbola? • How is it a conic section?

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