1. Hyperbolas Day 1 Standard Equation and the Graph

2. The Definition The set of all points in a plane such that the difference of the distances from two points, called foci, is constant. Does that look familiar?

3. The Picture and Equation (h,k) Transverse axis a a c c Tree Trunk

4. The Other Orientation (h,k) a a c c Happy/Sad

5. Day 1 is simply drawing the figure You need to draw the center, the tranverse axis endpoints (still a) and the asymptotes. We will use the “box method” (more later on that) to make sure that the shape is accurate. Do you remember what the relationship between a, b and c was in ellipses?

6. How to find foci This time, you take the sum of the denominators:

7. Lets go back to the definition: The set of all points in a plane such that the difference of the distances from two points, called foci, is constant. (h,k)

8. Remember: With ellipses, you move the number under each variable in that direction. It will be a very similar method with hyperbolas. Now is when we introduce the “Box Method”

9. The Box Method Move “a” units away from the center in both directions to form the transverse axis endpoints. Move “b” units away from the TA EP’s in both directions. Draw a box thru these 4 points. Draw asymptotes (corner to corner) Draw Hyperbola thru TA EP’s Plot foci

10. (0,0) Tranverse axis 2 2 2 2 2 2 -2

11. (1,3) 4 4 2 2 3 1 -3 3

12. Class work Solve Someone do it on the board!