Ellipse
Chapter Name : Conic Section |
Sub Topic Code : 104_11_11_05_04 |
Topic Name : Ellipse |
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Sub Topic Name : Standard Equation Of An Ellipse |
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Introduction
• Ellipse is set of points in a plane whose distance from foci add up to constant. • To solve practical applications on ellipse there is need of standard equation of ellipse which satisfies for all points on ellipse. In this section we derive standard equation of ellipse.
Pre-Requisites:
• Knowledge of equation of line. • Knowledge of ellipse. • Knowledge of special cases of ellipse. • Knowledge of eccentricity of ellipse.
Activity:
You will observe vertical major axis graph.
Real Life Question:
Which equation of ellipse is used to solve application involving elliptical orbit?
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. |
| Horizontal Axis | X-axis on the graph. |
| Vertical Axis | Y-axis on the graph. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Graph paper, Pencil | Determine the values of a and b as well what the graph of ellipse will look with the equation square(x)/36+square(y)/25=1. |
Real life uses :
Ellipses have many practical uses like in machine gears, architectural design, to design medical devices, in optics.
Places to visit :
Look for things in your house which are elliptical in shape?
Practical examples around us
| Examples | Explainations |
|---|---|
| Astronomy. | To give astronauts a visual landing zone they used shape of ellipse. Mathematical formula of ellipse gave them better chance of landing outside the predicted zone. |
What you learn in Theory:
Standard equation of ellipse satisfies for all points on ellipse.
What you learn in Practice:
Equation of ellipse is used in many practical applications like in medicine, astronomy.