Hyperbola Activity: Extending w/ Foci, Assymptotes & Point A

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Homework Help Overview

The discussion revolves around extending an activity related to hyperbolas, specifically focusing on finding the foci, asymptotes, and understanding the significance of "point a." The subject area is conic sections, particularly hyperbolas.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to recall methods for determining foci and asymptotes of hyperbolas and seeks clarification on the concept of "point a." Some participants suggest using measurements from points on the hyperbola to derive necessary parameters, while others mention the definitions involved in constructing the foci.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of hyperbolas. Some guidance has been offered regarding the number of points needed for measurements and the definitions related to foci. However, there is no explicit consensus on the methods or interpretations being discussed.

Contextual Notes

The original poster expresses uncertainty about the material, indicating a potential gap in knowledge or memory regarding hyperbolas and their properties. There may be constraints related to the resources available for the activity, as indicated by the mention of attachments instead of visual aids.

thimkepeng
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I need to extend this activity somehow, but I forgot this stuff already? I learned this a long time ago, I think this activity is too simple so can someone tell me how to find the foci, assymptotes, etc, and what the "point a" is for?
http://mste.illinois.edu/courses/ci399TSMsu03/folders/jmpeter1/Daily%20Assignments/Conic%20Sections/Hyperbola%20Paper%20Folding%28CI399%29.html
I put all I can do in the attachments since I don't have a camera or scanner:
 

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  • hyperbola.png
    hyperbola.png
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Physics news on Phys.org
Hyperbola is one of a class of functions known as "conic sections". Use google to find out about them.
Once you have three points on the hyperbola, you can make some measurements to determine the whole thing.
Constructing the foci etc is a bit trickier - you have to follow their definitions.
 
Simon Bridge said:
Once you have three points on the hyperbola, you can make some measurements to determine the whole thing.
It's three for a circle, four for a parabola, five for ellipse or hyperbola.
A normalised quadratic equation in two variables has five parameters. The classifications ellipse and hyperbola set constraints on the ranges of the parameters, but no exact relationships, so five degrees of freedom.
If you regard two hyperbolae as the same if they can rotated and translated to line up then there are only two degrees of freedom.
 
Sorry, I wasn't clear.
This method of construction specifies the foci at the start.
 

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