1. Hyperbolas
Topic 7.5

2. Definitions
Hyperbola: set of all points where the absolute value of the difference of the distance from any point on the hyperbola to the foci is contant

3. Two Standard Equations
Vertical Hyperbola:
Foci:
Vertices:
Asymptote Slopes:

4. Two Standard Equations
Horizontal Hyperbola:
Foci:
Vertices:
Asymptote Slopes:

5. Writing in Standard Form
Complete the square for both the x-terms and y-terms and move the constant to the other side of the equation
The first term will be the positive term between x2 and y2
Divide all terms by the constant

6. Example: Group terms Complete the square Simplify
Don’t forget to the negative nine!
Divide by Constant

7. Graphing the hyperbola
Put equation in standard form
Graph the center (h, k)
Graph the foci (look at the equation to determine your direction)
Graph the vertices
Graph the asymptotes (start at the center and use “Rise over Run”)
Draw “U” shapes that go through the vertices and stay in between the asymptotes

8. Example: 1) Graph Center 2) Graph Foci 3) Graph Vertices
4) Graph Asymptotes
5) Graph Hyperbola

9. You Try! Write the following equation in standard form, then graph it.