Ellipse
Chapter Name : Conic Section |
Sub Topic Code : 104_11_11_05_02 |
Topic Name : Ellipse |
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Sub Topic Name : Special Cases Of An Ellipse |
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Introduction
• Ellipse is set of points in a plane whose distance from foci adds up to constant. • Foci are two points inside an ellipse. • When foci of ellipse lie exactly at the same point then ellipse is called as circle. This is special case of an ellipse. • When semi-minor axis is zero and focus is equal to semi-major axis then ellipse is called as Line-segment. This is also special case of an ellipse.
Pre-Requisites:
Knowledge of equation of line.
Activity:
You will observe that string stretches same distance from pin to pencil to pin. If you put two pins at same point and draw then you will observe ellipse changes to circle.
Real Life Question:
Is spotlight special case of an ellipse?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Ellipse | Ellipse is set of points in a plane whose distance from foci adds up to constant. |
| Major Axis | Longest diameter of an ellipse. (At the widest part of ellipse). |
| Minor Axis | Shortest diameter of an ellipse. (At the narrowest part of ellipse). |
| Circle | Set of all points in a plane which are equidistant from fixed centre. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Board, Pins, String, Pencil. | Put two pins on a board. Tie string to two pins and insert pencil into the loop of string. Keep the string stretched so that you can draw an ellipse. |
Real life uses :
As we know ellipse has special cases of changing shape so it is used in Airfoils. Airfoil is a shape used in air plane wings which helps generate lifts.
Places to visit :
Look for things in your house which are elliptical in shape?
Practical examples around us
| Examples | Explainations |
|---|---|
| Tanks | Tanks transporting oil, petroleum are elliptical in shape and this gives them higher capacity. Hence they are more stable when being transported. |
What you learn in Theory:
Special cases of ellipse are Circle, Line-segment.
What you learn in Practice:
Ellipse is found in art and architecture, in designing lens and mirrors, and in airfoils.