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

[thimkepeng]

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:

 

[Simon Bridge]

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.

 

[haruspex]

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.

 

[Simon Bridge]

Sorry, I wasn't clear.
This method of construction specifies the foci at the start.