10.3: Hyperbolas

Here is a graphic representation of all the parts of a hyperbola:

The equations of hyperbolas are as follows. Don't forget that when talking about hyperbolas, the a does not have to be bigger than b. a will always be in front of the subtraction sign.

Center
The center will be (h,k)

Vertices
The vertices will be a units from the center point.
When the hyperbola is vertical...subtract/add a to the y value.
When the hyperbola is horizontal...subtract/add a to the x value.

Foci
The foci will be c units from the center point.
When the hyperbola is vertical...subtract/add c to the y value.
When the hyperbola is horizontal...subtract/add c to the x value.

Asymptotes
Use this formula to find the asymptotes:

 Graph the Equation. 
1. graph the vertices
2. count b from the center and draw points.
When the hyperbola is vertical...subtract/add b to the x value
When the hyperbola is horizontal...subtract/add b to the y value.
3. Draw a rectangle connecting these points.
4. Draw diagonal lines through the corners of the rectangle. These are your asymptotes.
5. Draw a hyperbola through the vertex, but not touching any of the asymptotes.

Math joke of the day:
Q: What's 2n plus 2n?
A: I don't know, it's 4n to me!